The 3 must-have platformers for the PSP :

Daxter

LocoRoco

Ratchet & Clank : Size Matters

But there are others to : Secret Agent Clank , Medieval Resurection , Death Jr 1/2 etc :)

For long car trips, its a tie. You would think DS is better due to better battery+brighter screen, but for $15 you can get a power adaptor and charge PSP in the car, which gives you a 3rd brightness setting,thus being just as bright as DS and having infinite battery life.
PSP offers more features, a bigger screen, better graphics, (imo) superior controls, (imo) better games, and a smaller library. Game wise it is a bit like the N64, but with fewer mind blowing titles and more 3rd party support. There are roughly 70 PSP games worth owning, so depending on your tastes, there should be at least 15 games you like, even if you are very pikcy and only play JRPGs and SRPGs or something.
features- online browsing, playing on your TV, movies, music, skype (imo useless) can hack to play older games (imo useless, get sega genesis collection and skip the $40 and 10 hour hassle)
I will post my list of recomnended games hsortly.

I should mention I bought a DS at launch and bought a PSP about 3 months ago, and I like PSP much better. If your friends love playing Teris DS and Mario Kart DS, join them. Those are some good times :D

Castlevania: Dracula X Chronicles is another great 2D platformer while Daxter and Dead Head Fred are fine 3D platformers.

Platformers? I love em, along with HRPGs and SRPGs, and there are a bunch. Off the top off my head good platfomers-

LocoRoco
Ape Escape: on the Loose
Daxter
Rachet and Clank:Size Matters
Mega Man Powered Up!
Sega Genesis Collection (contains sonic 1 and sonic 2)
Sonic Rivals
All these games can be had for $20 or less
also
Sonic Rivals 2
LocoRoco 2
are available (locorco this fall, rivals is $25 online and $30 in stores)
9 high quality platformers... quite enough to buy the system for imo.
also, Disgaea afternoon of darkness, Jeanne D'arc, and Fina Fantasy Tactcis: the war of the lions are all incredible SRPGs.
Kingdom hearts: birth by sleep is looking like the orignal KH graphically.
Monester hunter freedom is supposed to be excellet.
Patapon is one of the best games I have ever played, is only $20 new, and a sequal is coming soon!

Well, I said to get a DS in the other thread and I stand by that.
But if you are looking for the pro's of a PSP over a DS (from a person that owns the latter and has spent a large amount of time with the former):

1) Screen. PSP screen is gorgeous, and much better then the DS. It's also bigger

2) It's a multimedia device out of the box. DS can be a multimedia device aswell, but not out of the box

3) It really does feel like you've got a PS1.5 you can take around anywhere (which is a pro if you like graphics, and I think it's a pro)

4) I stand by what I've said that DS games library > PSP games library. But there are a few standout titles on the PSP. Crush, Loco Roco, Patapon, Crisis Core and GoW really are great games and the first 3 are rather unique and fun.

5) Analog stick. Basically my only gripe with the layout of a DS is the lack of one. Sure the touch screen/stylus sort of compensates for that, but it'll never feel as good as a analog stick does (particularly because you sacrifice visibility of the lower screen to use the stylus.

6) PSP speakers are much better then the DS lite's.

PSP has plenty of games at an affordable price. This was done beforehand for my personal use and has been modified for you. It has been highly researched and is reliable. (pricing may vary a bit, as amazon prices fluctuate, and the pricing data is about 2 months old)

PSP games to buy – I have also rated every game for you :D

PSP Daxter Entertainment pack Slim system ($200- comes with PSP, Daxter, memory card, family guy UMD)

Final Fantasy Tactics: The War of the Lions ($28) (SRPG) (10/10)
Patapon ($20) (strategy music game) (9/10)
Daxter (comes with PSP) (platformer) (8/10)
Sega Genesis Collection ($12) (Sega compellation) (9/10)
Patapon 2 ($40) (rhythm) (9/10)
God of War: Chains of Olympus ($27) (beat em up) (9/10)
LocoRoco ($24) (platformer) (9/10)
Tales of Eternia ($40) (RPG) (9/10)
LocoRoco 2 ($40) (platformer) (9/10)
Jeanne D’arc ($20) (SRPG) (9/10)
Disgaea: Afternoon of Darkness ($22) (SRPG) (9/10)
Harvest Moon: Boy and Girl ($15) (sim-RPG) (9/10)
Ratchet and Clank: Size Matters ($10) (platformer/shooter) (8/10)
Riviera: The Promised Land ($27) (RPG) (8/10)
Star Ocean: First Departure ($40) (rpg) (8/10)
Star Ocean: Second Evolution ($40) (rpg) (8/10)
Ape Escape: On the Loose ($6) (platformer) (8/10)
Burnout: Dominator ($8) (combat racing) (8/10)
Grand Theft Auto: Vice City Stories ($9) (sandbox) (8/10)
Valkeryie Profile: Lenneth ($22) (RPG) (8/10)
Super Stardust Portable ($40) (shoot-em-up) (8/10)
Grand Theft Auto: Liberty City Stories ($13) (sandbox) (8/10)
Ridge Racer ($10) (racer) (8/10)
Final Fantasy 7: Crisis Core ($29) (beat em up) (8/10)
Metal Gear Solid: Portable ops ($29) (stealth action) (8/10)
Metal Slug Anthology ($20) (action compellation) (8/10)
Space Invaders Extreme ($20) (shoot em up) (8/10)
Castlevania: The Dracula X Chronicles ($19) (action) (8/10)
Sonic Rivals ($10) (platformer) (7/10)
Field Commander ($12) (strategy) (7/10)
Generation of Chaos ($18) (SRPG) (7/10)
Aedis Eclipse: Generation of Chaos ($15) (SRPG) (7/10)
Spectral Souls (SRPG) ($20) (7/10)
Spyro the Dragon ps1 classic ($6) (platformer) (7/10)
Yggdra Union ($40) (rpg) (7/10)
Tales of the World: Radiant Mythology ($33) (RPG) (7/10)
Mega Man Powered Up! ($10) (platformer) (7/10)
Mega Man Maverick Hunter X ($12) (platformer) (7/10)
Sonic Rivals 2 ($17) (platformer) (7/10)
Crazy Taxi Fare Wars ($9) (racer) (7/10)

Games you may want I am not interested in: (thus ratings are scrambled)

Flatout: Head on ($15) (destruction) (7/10)
Star Wars Battlefront: Renegade Squadron ($20) (TPS) (7/10)
Pursuit Force ($8) (destruction) (7/10)
Twisted Metal Head On ($8) (Destruction) (7/10)
Secret Agent Clank ($40) (genre mishmash) (7/10)
Wipeout Pure ($6) (racer) (8/10)
Wipeout Pulse ($22) (racer) (9/10)
Lumines 2 ($11) (puzzle) (9/10)
Lego Star Wars 2: The Original Trilogy ($11) (platformer) (7/10)
Lego Indiana Jones ($24) (platformer) (7/10)
Pursuit Force: Extreme Justice (destruction) (7/10)
Gradius Collection ($12) (shoot em up compellation) (7/10)
Me and My Katamari ($22) (fantasy adventure) (7/10)
Crush ($12) (puzzle platformer) (8/10)
Innocent Life: A Futuristic Harvest Moon ($18) (sim-RPG) (7/10)
Wild Arms XF ($29) (SRPG) (6/10)
Final Fantasy Anniversary Edition ($18) (RPG) (8/10)
Killzone: Liberation ($10) (FPS) (8/10)
SOCOM U.S. Navy Seals Fireteam Bravo ($6) (TPS) (8/10)
SOCOM U.S. Navy Seals Fireteam Bravo 2 ($10) (TPS) (8/10)
Legend of Heroes ($20) (RPG) (6/10)
Legend of Heroes 2 ($24) (RPG) (6/10)
Legend of Heroes 3($15) (RPG) (6/10)
PaRappa the Rapper ($8) (music) (6/10)
MediEvil Resurrection ($11) (brawler) (6/10)
Metal Gear Acid ($15) (strategy) (8/10)
Ape Escape Academy ($8) (mingame) (7/10)
Metal Gear Acid 2 ($10) (strategy) (8/10)
Tekken - Dark Resurrection ($12) (fighting) (9/10)
Medal of Honor Heroes ($12) (FPS) (8/10)
Medal of Honor Heroes 2 ($20) (FPS) (8/10)
Heatseeker ($13) (plane combat) (6/10)
Star Wars Battlefront 2 ($12) (TPS) (7/10)
Hot PXL ($5) (microgame collection) (6/10)
Capcom Classic Collection Remixed ($9) (Capcom compellation) (6/10)
Capcom Classic Collection Reloaded ($10) (Capcom compellation) (6/10)
Hot Shots Gold: Open Tee ($11) (Golf) (8/10)
Hot Shots Gold: Open Tee 2 ($40) (golf) (8/10)
Worms Open Warfare ($16) (strategy) (6/10)
Worms 2 Open Warfare ($22) (strategy) (6/10)
Namco Museum Battle Collection ($12) (Namco compellation) (6/10)
Syphon Filter Dark Mirror ($9) (stealth action) (8/10)
Syphon Filter: Logan's Shadow ($22) (stealth action) (9/10)

You are partially right, but make the PSP out to be worse than it is.

1. Battery lasts 4-8 hours. On max sound max brightness, expect 4 hours. On min brightness no sound, it lasts 8. Mine usually lasts 4.5, as I play on 60% sound max brighness. Expect 4.5-6.5 realistically, as you cannot see with min brightness, but medium brightness is fine.

2. There are lots of great original games and lots of great remakes. There are some lame ports yes, on my list of lots of games, I include remkaes but not ports. Final Fantasy Tactics: The War of the Lions and mega man powered up are both fantasic remakes. Disgaea afternoon of darkness is a port, but it is not lame; it is one of the PS2's best games and one of the best SRPGs ever, along with tactics ogre and final fnatasy tactics. Origianl good games include: Sonic rivals 1 and 2, monster hunter freedom 1 and 2, syphon filter logan's shadow, god of war chains of olympus, final fantasy 7 crisis core, wipout pulse, wipout pure, locoroco 1 and 2, patapon 1 and 2, and many more. See my massive list :D

3. See my list. Plenty of origianl games. There are about 20 original games that are 8.5 or above, and many more than that. Plus, ports/ramkes are fine if you havn't played the original before or really liked it and want to play an enchned version on the go!

4. I really like the analog stick. It is responsive and works well. After about 2.5 hours of gaming it makes your thumb muscles hurt for a while and you need to stop... but most 3D games can also be played with the -pad, and that doesn't hurt. And if you are on a car ride ect, you can switch to a 2D games (there are lots) or movies/music to give your thumb a rest. DS lites terrible D pad makes your tumb hurt after about 3 hours anyway. (DS lite>DS origianl, I have both, but I keep orignal around even though top screen is crakced becuase it is much better for GBA games as its D pad is much much better)

5. Buy the Ice silver Daxter pack like I recomend and you won't get any fingerprints. Be sure to buy a $5 screen protector- that is a criticsm itsamii forgot- screen scrathes easily, but is fine with a protector which is cheap to get anyway.

6. 2 foot or less drop and PSP is ok. I don't recomend lettting people borrow it or walking around using it though.

Eh... I kinda disagree. Sure PSP has M rated shooters and such the DS lacks, but it also has lots of fantasctics shildrens games and 2D rpgs ect. MY brothers 12 year old friend really wants one, but he cant offord it quite yet. Since the rice dropped though he has been saving up.

DS had great 1st party support in year 1 and 2 and then it dropped off. Now it has good RPG remakes, quirky games like that offer somthing new like EBA, and cooking/casual games that don't interest hardcore gamers at all.

In the end I think its good to have both, but if you can only have one and you don't have people to play multiplayer DS with, PSP is a much ebtter choice due to its game library.

If you want a portable PS2 get a PSP, If you want a unique and new way to play games get a DS.

Many good things that can be said about a PSP have been said already (Media capabilities, graphics, brighter screen, better speaker, etc)

PSP is more fragile than PSP, but than DS is not that much sturdier, either.
They're both handhelds like cell phones. They can both break easily, of course, if you drop them. I recommend buying NERF for either one (Though buying a case for DS prevents you from playing GH:OnTour, if you care)

As far as sound, neither one is all that great. PSP is good enough to listen music and movies to but it's still a handheld, not a portable DVD player.

PSP online isn't all that great either, but like I said it's a handheld.
The fact that you can surf online though is a plus considering DS does not have one. (They have DS Browser but it's discontinued, I think, due to its craptastickness and it's made by Nintendo!)

PSP Music somewhat annoys me; it does not let you have playlists (Good thing most of us probably have a damn MP3 or hell even an MP4 player - one that can also read .avi).
There are some 3rd party media player out there for DS but compare to PSP, it comes up real short.

Compare to the many things PSP can do vs DS, DS has two things PSP cannot do/handle: Touchscreen and Guitar Hero: On Tour

If you can overlook their flaws, then it all depends on your taste.
And also, there are a number of ways and things you can buy to which you can adjust to these flaws.
It just comes down to your pickiness.

I feel it's all apples and oranges to me.

Now,
None of the people above lies. PSP is great for media - Music, movies, game demos, photos, and homebrew.
It having a bigger screen and better speaker than DS helps you fulfill and satisfy enough of what you need when you're mobile.

I personally bought my PSP because I have a 4gb M2 memory card for my Sony Ericsson phone... I just recently bought an 8gb M2 (comes w/ an adapter) for about $50. Damn cheap for its size.
As far as games, Nintendo has great 1st party titles - no doubt; and DS has enough 3rd party support (Not to mention, enough RPG’s)

PSP, though, has amazing games like FF: Crisis Core (and upcoming Dissidia:FF) and God of War, IMO.
Which DS at this point could never do. Even Yu-Gi-Oh! DS and Warhammer DS are incomparable to the PSP versions.

I love my PSP because you can listen to music, store photos, plays demos and games, and watch movies - all in one!
And if you’re around a wi-fi hotspot, even surf the ‘net.
Not to mention, you can modify its themes and have skype and internet radio.

Comparing PSP to DS is unfair. PSP is a PS2 in your hand while DS is a N64 in your hand.