I can't compare the PSP to another consoles because it was my first console, and I loved it on it's time, I had a DS on the same timeframe, and if I try to compare both, I think I enjoyed the PSP more, but the DS had more games that I feel like were must have's (POKEMON, I was addicted back in the day, don't really care for it anymore tho.)

Today I have a PS Vita, never touched my PSP or DS anymore... I just love the Vita so much, it is everything the PSP should have been in its time, it just doesn't have as many third party support, but IMO it already have more games that makes it a must have console! Like: 

Gravity Rush - one of the best games I've played in my whole life, Kat is sooo charismatic, pretty, cool, ... The city in the game is so immersive and amazing to explore (wish they would give more options to do there but it's good enough for the first game), the game history is amazing and so intriguing, really curious on the second game! Gravity is so freaking cool, gameplay is awesome! (Only hard thing was the Gravity Slide, but you get used to it if you play hard enough)

Tearaway - oh man that's a game that relly reminds me of how much I miss playing 3D platformers from PS1 N64 Era! It's an amazingly beautiful world, with so much stuff to collect, people to help and have fun, If you enjoyed Banjo & Kazooie or Spyro this is a must have! Also it uses the PS Vita interactive functions in such an amazing way!

LittleBigPlanet Vita - This was the best version of any LBP game, it's amazing on the Vita, makes great uses of it's functions, have a lot of funny minigames, it's simply the best place LBP will ever be!

Persona 4 Golden - Didn't play it on PS2 Era! It's such an amazing game, you get so into the story, you really feel like you're part of it!

Sly Cooper Thieves In Time - Another 3D platformer that looks so amazing on Vita! It plays perfectly on it, and it's really cool to explore the games's cities!

Killzone Mercenary - During PSP Era I never thought FPS could ever belong in a portable, not having  dual analog sticks to play really damaged the genre on portable consoles, I promised myself I would never play a game again using triangle, circle, square, x to move the camera, it just felt so wrong, I could never get used to that! Killzone Mercenary, was simply the perfect FPS conversion to a portable system, it looks just as amazing as PS3 games, and I kinda feel like it's the best game in the series (draw with Killzone 2)... just know that the MultiPlayer is it's gem, didn't really enjoyed the Single Player Campaign.

Uncharted Golden Abyss - PS3 quality titles can be made on the Vita and this is a living proof, the game is really beautiful, makes interesting use of Vita capabilities, have cool puzzles, but to me the history was too long to do the same thing and I couldn't finish it...

Sound Shapes - This game is amazing 2D platformers, levels are really well made, and has many user created levels.

PlayStation All-Stars Battle Royale -  Well PS1 has been the first console I really owned and had my own games (had a Megadrive before that, but I can't consider myself a "gamer" before i was 5) I really enjoyed it's games like Crash, Spyro, Medievil, Parappa The Rapper, after that I continued to own every SONY console, the PS2 with Ratchet & Clank, Jak & Daxter, Sly Cooper and God of War and PS3 with LittleBigPlanet and others, the possibility in this games was such a blast to imagine, and the Rival Stories were so fun to miss it, the game ended up having too little content to be the true "SMASH" it could be, but was good enough for some fun!

Soul Sacrifice - 3rd person action RPG, has such a cool story, awesome online mode, had a lot of fun with it! The game has a lot of content... Just wish it had more open world and exploration, but it gave me the feeling I was exploring through the book and that gave me a lot of fun...

Destiny Of Spirits -  cool free to play game, get me very addicted... but sometimes I get sick and tired of it, and then I want to play it again... LOL but it's a nice game! It just reached 750k downloads, Maybe they can make it a "real game" someday, it has enough content to... :)

Muramasa Rebirth - Yes Vita rocks for it's Asian stuff mostly! This game looks amazingly beautiful on Vita screen, I want more HD versions of Vanilla games on Vita!

PSOne Classics - Well, PS1 was totally one of my favorite consoles ever it had so many games I couldn't ever finish! When I put the on PS3 their graphics looks so blown that I couldn't get used to it, but on Vita it's like they're on the best place they could ever be! I can't believe with Vita I could finish Tomba!, Tekken Classics, Gex, Rayman, I was luck enough to buy Crash Team Racing during the week it was available for Vita, and it's so cool to be able to play games I never finished or played like Wild Arms, Arc The Lad, Legend of Dragoon and Vib-Ribbon)

That~s why I think Vita is the best upgrade on PSP to ever happen, really hope it can shine sometime!

I like the PSVita, but it's support is so dead. That's why I keep my PSP, because it was actually supported, and it had amazing games, despite it's hardware constrictions.

PSP was a really great system with a terrible analog stick (thumb stick).
Played some INCREDIBLE games on it as listed above. Wish it had trophies

I still regularly use my PSP. In fact, including PSOne Classics I likely have more titles for it than any of my other consoles. It's certainly my favorite handheld, although the original Gameboy and the DS are probably more influential.

I actually opted to get a PSP with the money I could have spent on a smartphone. I do not regret this decision one bit; I got way more value out of a $40 game every other month than I would have ever gotten out of a $60 a month data plan--especially when WiFi is everywhere. I will probably keep my PSP until it breaks.

The sad thing with the Vita was Sony made it entirely too pretty and powerful. You don't actually want production values on a handheld to climb too high; most devs for them work on AA budgets at best. This is a magnificent example of know thy business partners. I really hope Sony tries the handheld thing one more time. A smartphone with button inputs and an SD card slot would be fantastic, especially if Sony doesn't try to murder the bankers again.

That's surprising since the PSP remade ALMOST ALL the FF from the NES/SNES days. They all look modernized too. And it also had remakes of Mega Man X and the OG Mega Man for NES. That and many throwback games from Capcom, Namco, and even Sega in collection pieces! But I guess if you use it to emulate, that last part is useless.

I love my 3DS too but ironically I find myslef playing my DS games more on it. But lately Smash has taken up all my time. Really though, as soon as I get my PSP i can clearly see it taking my 3DS place for like a good 3-4 months though.

My PSP was magic, even more so after i got CW working and put a bunch of SNES classics.

Don't miss out on Star Ocean: First departure, Dissdia 2 (it has the story of the first one as well) and kingdom hearts BBS.

The PSP is by far one of my least favourite consoles.

I would rate the handheld consoles like this:

1. DS/3DS
2. GBC
3. GBA
4. PSP

You see that's a really impressive list. I REALLY WANTED TO GET A VITA!! But to tell you the truth I got the 3DS just to play old DS games (Pokémon SoulSilver, Fire Emblem: Shadow Dragon, The 2 Zelda's) I missed out on, while waiting for that 3DS title that makes me want to buy one (Fire Emblem: Awakening). But playing the Classic DS games outweighed playing the newer 3ds games.

If the Vita was backwards compatible, there is no question I'd get it (as I would think MANY MANY others would too). But right now the 8 games I want to get on the PSP outweigh the ones you describe. Maybe when I'm done with my PSP i'll borrow my bros (or maybe even trade it for my Nintendo 3ds, he's willing to trade his Vita for it ), because that list is definitely something I would want to explore later.

Totally agree with everything you said on the Vita. Instead of wasting on the best tech available, they should have spend that money on making it backwards compatible! I swear I feel it would have sold at least 20m if it was backwards compatible. The PSP library warrents it! The reason why the PSP had so many games is because production was so low! IMO they completely tried to throw a Strong Haymaker punch to the 3DS by making it so beefy, but it COMPELETY missed it's mark.

Yeah I feel the same way, hence why I'm not buying the PS Vita probably until it goes retro (ironically like the PSP). That way it'll have well established games that I'd be more than happy to get...