It depends. Bot systems have different games. Pokemon's one of the most popular strategy turn-based game for DS only. And the DS has some pretty cool games that have WiFi. As for PSP, it's got some pretty good games too like Dissidia Final Fantasy, but usually their multiplayer is Ad-Hoc (wireless, close range) with few having Infrastructure (WiFi).
if u r older and u can play mature and teen games totally the psp, the online is oka, but it has really good sports a good action games. also the psp is great because you can get movies, tv shows, music, internet browers, pics, skype, camera, and more.
the ds is for smaller kids because it has e and e 10+ games.