I do agree that the PSP is about done. Granted, there's a number of AAA titles that you could pick up, ranging from RPGs (even niche SRPGs), tactical shooters, to futuristic racing. Most of these could be had for 10~20 bucks regardless if it's used or from the PSN store. I love my PSP to bits and some of the recent games have been pretty sick (God of War: Ghost of Sparta, MGS: Peace Walker, Dissidia Duodecim [Final Fantasy fighter], Final Fantasy IV collection [including the Wii Ware stories], Patapon series, etc.) so you won't be waiting around for a real game library to show up. For T to M-rated games, the PSP has you covered (and yes, there are a few family-friendly games too if desired such as Patapon/Loco Roco.)
As for the 3DS, I tried it for a few hours when my dorm buddies picked it up, the 3D did strain my eyes after 20~30 minutes of play time, but that's just my personal experience, wasn't too crazy about the controls. Only real reason not to get the 3DS would be 1) the amount of "decent" games offered, 2) possible eye strain, 3) Nintendo will do a revision in the future like they did with the GBA and DS, possibly at a lower price.
The DS Lite didn't cut it for me other than a few titles (Mario Kart, Chrono Trigger, Megaman series), but the PSP is a smart and relatively cheap choice. My vote is for that.
...and who needs a 3DS when Sony's NGP/PSP2 is right around the corner?
EDIT: General overview of some of the better games:
http://psp.ign.com/articles/102/1023970p1.html