I'm sorry I didn't read every post on here but I think I can help. I own a ds lite with an r4, psp slim with 5. something m33 cfw, jailbroken iphone 3gs. Anyone that says dsi apparently doesn't know that the battery lasts 2.5 hours. DON'T EVEN THINK DSI. It now comes down to PSP, DSL, Itouch. If you want to play any games, itouch is out because it can't support off screen buttons (realistically). Sooooo ds or psp.........it boils down to this. To their credits respectively,
1) DS has: zelda ph, diddy kong racing, ff3&4, chrono trigger, new super mario, pokemon, metroid hunters, animal crossing megaman, mario 64 and can play music crappily. You need a flashcart (r4 m3 etc...) and depending on the cart you can have a micro anywhere from .5 gigs to 16 gigs.
2) PSP has: CRISIS CORE, DISSIDIA, GOD OF WAR, GITAROO MAN, MEGA MAN MHX, TALES RM, TALES OF VS, MONSTER HUNTER, CAN EMULATE CONSOLES UP TO PSX (SO FF7,8,9 XENOGEARS, you get the point), HAS VIDEO OUT, IS A MEDIA PLAYER, SEXIEST SCREEN ON THE MARKET, FULLY CUSTOMIZABLE, terrible storage.
If you want another way to look at it, a crappy touch-screen wii, or a sub-par ps2. Oh and one other thing. I played ds games on the psp. I did't play psp games on the ds.
Hope that helped