Welp, soon this topic will start with the flame wars between the majority of DS loyal, and the vocal minority PSP entheusiast, spearheaded by Hunter_Alien and a few others, but lets not get ahead of ourselves.
It's just silly and insulting to the DS to say that all it has is Poke'mon games, just like it's silly to claim that the PSP is a failed system, or "has no games."
Here are the important points I can make:
The PSP has a slight lead in the number of 80 plus games on gamerankings. That is certainly cherrypicking, and yes, most of those games are pretty crappy, like MLB:06 The Show, but I mention it because it's a PSP talking point.
The DS and PSP libraries are vastly different.
IN MY OPINION: Most traditional handheld gamers who perfer Japanese support, and the wide range of genre titles, would be better off with the DS. This simply stems from the large amount of 3rd party support, particularly JRPG's, the DS has amassed due to sales. Just looking at the 08 lineup for the DS, or the things that is has release so far this year, the PSP can't compare, unfortunately. Already we have Advance Wars:DoR, Ace Attorney, Laytons, Dragon Sword, CC, and other games.
IN MY OPINION: If you're looking for a more "Playstation" experience, or really, a more "home console" experience, with added abilities like MP3 player and movie functionality, then the PSP is definately the right choice. However, this year, the system has shown some quality support from a software perspective, with GoW, Papaton, and Core Crisis being premiere in its lineup.
In the end, it comes down to taste. Both systems have plenty of reasons to buy them, and both systems have enough great games to keep any gamer busy, who hasn't bought one yet, for the next two years, easily, by itself.
The actual quantity of quality titles, PROBABLY resides with the DS, but why try to compare them when they are so close? Why try to lable one as a "Poke'mon system" or one as a "sports game" system? That's just flame bait. The fact is, both systems have their share of games aimed at an adult audience, and both systems have their share of sports games, and both systems have at least passable games from most genres.
There is no real anwser, it's a matter of taste.
Obviously, being a huge fan of Japanese style games, I find both systems have must play games, but the immediate future has me leaning far more towards my DS for these reasons:
Rondo of Swords
DragonQuest IX
Valkyrie Profile 3
The World Ends With You
Kingdom Hearts
Etrian Oddessey 2
Soma Bringer
NG:Dragon Sword
Tales of Tempest
Tales of Innocence
Final Fantasy Tactics Advanced: A2
Fire Emblem remake(with Marth)
Professor Laytons and the Curious Village
Advance Wars: Days of Ruin
Apollo Justice: Ace Attorney
Professor Layton and Pandoras Box
Castlevania DS part 3
FF:CC
Disgaea: Hour of Darkness DS
I don't have the PSP list offhand, but it is also impressive, imo, just not quite as impressive.
I hope my 2 cents had added to this topic and not detracted from it.
I just wanted to add, in response to the post above mine, I think that the DS has a significant lead in JRPG's, due to upcoming titles, but particularly, I think it has a lead and is not trailing in SRPG's right now, just because of the Advance Wars series, which is amazing, along with the fact that Fire Emblem, Rondo of Swords, and Disgaea are hitting the DS pretty soon.
I would say that FFT is greater than the Advance Wars titles by itself, however, it is a port, and I can't see it giving the PSP the edge in current tactics, particularly with the pretty awesome list of upcoming DS tactics support gaming.
However, I do feel that the number one reason to own a PSP is because Final Fantasy Tactics: The Lions War is avaialable for the system.
As for action, I hate to say it, but I think that goes to the DS as well, because of the Castlevania games, Contra, Ninja Gaiden, and quite a multitude of other amazing action games availble for the system. A lot of earlier games are often overlooked, with the DS. Of course, this is all just my opinion, which I'm sure vastly differs from the next guys.