Games are more fun on DS. Graphics don't make the game.
Your first sentence is entirely your opinion and is fine. I don't see how the second one relates very well with this thread.
I have both. Each have their ups and downs but I don't regret either purchase. I also have friends who have PSPs who are interested in the DS (and a few vice-versa). After I've beaten FF3 to death (well some jobs aren't maxed yet) I've took a break from it and picked up some PSP games. Picked up and currently playing Mahjong Fight Club since its already in Konami's The Best budget line and I'm waiting for the Pokemon DS games and Phoenix Wright 2 (GS2).
That graphics argument thing... While I could play mahjong with Yakuman DS (and get my ass handed on wifi) I'd like a more mature and stylish feel while playing so I went with MFC on PSP instead. Of course both has the same gameplay (other than the AI which I don't care since I suck) As PineappleH said, games nowadays need both graphics and gameplay.
(Oh and before some guy says MUDs, I think MUDs which are online can mostly depend on the community, I mean look at this forums... why the hell are we wasting time here lol.)
While only somewhat related to the topic: I think people in the closed mindset that one has to be better than the other should be a thing of the past. Jeez, sales charts or whatever shouldn't dictate what people enjoy. While stating your opinion is fine and all, please convey it in a proper manner that doesn't look like you're arguing with other kids in the cafeteria during your lunchtime.
EDIT:
I started with psp because of 1 reason, Initial D Street Stage. Then I researched about downgradability and got rid of my ta-082 and got another white non-ta082 that's now a 1.5. Then I got another black psp for the hell of it to use as a beater to go. Eventually (quickly), I got bored of the games on psp, just pretty to look at mostly. So then I tried hard to get a ds lite in Japan while I was there...and that was seriously impossible. This was when ds lites first were released in Japan right before Golden Week. Now I got 5 ds lites total and my psps collect dust. I just lost interest in psps after I defeated Bunta in Initial D.