This should really be in the Akihabara section methinks.
But to answer your question, each has it's own strengths and weaknesses as you say. The PSP is obviously, a very sexy machine. Wide screen, mp3 player, movies, internet and depending on the game, can match the PS2 in terms of graphical power. Some of the best games I would say are Metal Gear Solid : Portable Ops, GTA Vice City : Stories, Syphon Filter and Lumines. Weaknesses though are that usually, most games are almost carbon copies of those on the PS2 and so, there isn't many distinctive, original titles out there (bar the titles I mentioned)
The DS is a genius, wonderful machine with many truly great original games. Play Phoenix Wright and I can guarantee you can't help but smile. Some of the best titles that I can gather of it are New Super Mario Bros, Brain Training, Zoo Keeper and Elite Beat Agents. Most obvious disadvantage that some would say is the consoles lack of graphical prowess, but I don't care about that really. At the end of the day, the gameplay is what matters, and for the most part, they really do deliver.
I don't know which one I'd recommend over the other tbh. If you want a machine that can do other multimedia services then go for the PSP. If it's the actual gameplay you want, then go for the DS.