Well, I am a BIG Nintendo fan, and I have both systems. I like the PSP much better.
DS has more games, but when it comes to games I really want, DS has about 30 while PSP has about 35. There are about 50 games total I could see getting for PSP and about 85 games I could see getting for DS.
PSP has a poor battery life (about 5 hours) but if you are on a ship recharging should be no problem. PSP has some games you can play for a lonnnnggg time. Here are my recomendations:

PSP
Disgaea: Afternoon of Darkness (can last 100's and 100's of hours if you want to get your people to max level- 9999. SRPG)

Final Fantasy Tactics: The War of The Lions (should last 100 hours, more if you try to replay with having your people as low of lvl as possible. SRPG)

Grand Theft Auto: Liberty City Stories/Vice City Stories- you should know how this goes.

Jeanne D'arc (its a good SRPG, I don't have it but it should last at least 30-50 hours)

Sega Genesis Collection- lots of old Genesis games, including golden axe, sonic 1 and 2, and many others. Should last a while.

Metal Slug Anthology- lots of metal slug games. Should last a while

Tales of Eternia- EU only game, can be imported. Good RPG, last a while.

I also really like Patapon and Daxter. Havn't played them, but I hear rachet and clank size matters and god of War chains of olympus are good. Also Killzone: Liberation is supposed to be good. Space invaders extreme looks good, and its only $20.

Would you be so kind as to produce this quote in context?

And, after you've done that: are we supposed to ignore the hundreds of other, non-Nintendo, DS games?

DS!! its awesome and fun!!

come on a DS is the fastest selling system...that means its awesome!!

    the other games like Poniez 2, my dogz 2, bratz and movie games?   Honestly I can't think of more then 3 or 4 adult oriented games on the DS (brain age and related games are more or less it)

The DS is the definition of how a succesful system should be.

Nintendo DS is the system with the most third party support. It has more support from third party than the console systems.

Yeah, it has a lot of casual, but, it also has a lot of hardcore. The DS, together with the PS2, is an example of how a succesful system should be: a lot of hardcore games plus a lot of casual games.

Too bad that in this site, specially PSP only owners promotes the DS as a casual system only, but by fortune, 70 million of people are enjoying their DS.

And I honestly can tell you, as a PSP and DS owners, that the Wii has a lot of better games... specially RPG's and unique games that can't be done on the PSP (Elite Beat Agets for example).

They said: Crisis Core, and I say:Dragon Quest IX

God of War, and I say: Phantom Hourglass...

PSP has Metal Slug Antologhy and the DS will have in a few months the brand new Metal slug 7, exclusive.

PSP Jeanne de Arc... DS has The World Ends With You

PSP has a Castlevania remake... DS the new Castlevania DS order of Ecclesia

PSP has two Megaman remakes: Powered Up and Maverick... the DS has two new 2D sidescrolling Megaman: Megaman ZX and ZX Advent

And also a lot of point and click adventures not posible on PSP because it doesnt have a touchscreen: Hotel Dusk, Ace Attorney series, Profesor Layton, Touch Detectives, Nancy Drew, Trace Memory...

Plus, Chrono Trigger

 And of course: Nintendo first party games...

Plus, no load times, a battery that last at least the triple than the PSP batery, and a much brighter screen.

DS succes, and DS outselling every other current system every month is because the game selection is huge.

Check this thread. It takes a few seconds to load all the images, but you will love the thread.

I hope this link help you: http://www.neogaf.com/forum/showthread.php?t=222049

DS, because the most of the guys arguing for PSP are idiots. Do you really wanna be in a group with those kind of people?

Check this: http://www.neogaf.com/forum/showthread.php?t=222049

If you are going to be a troll, at least be a good one, not an uninformed one.

And yet another troll artfully vanquished--it's just too bad they have such zombie-like tendencies.

I am a bigger DS fan but it sounds like from what you mention you may be a bigger fan of the PSP but then you mention you like Pokemon which is throwing me off. If your wanting the same sort of games as you get on the PS3, God of War and Metal Gear Solid for instance, then your definetly wanting a PSP. If you want Pokemon and Mario your definetly a DS person. Perhaps you can give us a better idea of what sort of games your interested in.

Ninja Gaiden Dragon Sword, Final Fantasy Tactics Advance 2 should be (has a very simplistic story unlike the classic original), Trauma Center Under the Knife, uh... uh... Brothers in Arms DS? That last one got crap reviews though.

A agree, PSP has better games. DS certainly has more though, and has something for everyone.

According to Meta Critic, DS has 98 75 or above rated games, while PSP has 113. Quantity over quality. DS is kinda kiddy, but IMO its worth having becuase the 1st party is great. Too bad it has all but dried up. Also, old first party games are roughly $25 on amazon so you won't save much. Alot of PSP games are really cheap though.

To OP- since you are in the navy I think you would like PSP better. It has more violent games which I am assuming you like (I persoanlly don't like em, but I love platforemrs and quiky games and SRPGS, which PSP has alot of. Honestly PSP has great games for everyone except casuals, but thats where the money is nowadays)

If you get a PSP, get a screen protector. The screen scrathes easily. Get the Red or Silver PSP. Black shows smudges.