My kids love different games at different times. They get tired of them and play others, then pull out the "old" ones again later on. They have gone between Indiana Jones Lego, Star Wars Lego, Pirates of the Caribbean, and any/all of the Mario games. They don't tend to care for the "educational" ones like Brain Age or any of the memory stuff...
Yoshi's Island was always a favorite of theirs, until my daughter lost it about a year ago. They also enjoy the New Zealand game. Daughter doesn't know it yet, but she is getting the one that teaches Spanish for Christmas... (she told me she wanted Rosetta stone so she could finish learning Spanish, too much $$ -- she is 8 yrs old). lol
I chose Nintendo DS b/c they seem durable, were priced better than PSPs, and had plenty of accessories available to pack/protect and carry them. Plus, since we were buying 2 eventually (2 kids) pricing mattered. Don't know about PSPs, but with the nintendo, they can download-play against each other (each on their own handheld- they are wirelessly linked). Also, the charges seem to last a good long time.
Hope this helps.