Persona 3 FES is an amazing PS2 game that ate up 300 hours of my time. Persona 4 came out earlier this month, but I haven't picked it up yet. It is also on the PS2. A slightly older PS2 favorite of mine is Star Ocean: Till the End of Time, to which I devoted about 250 hours.
The PSP is best used for simple games like Loco Roco and Patapon, but feel free to try out Crisis Core: Final Fantasy VII.
Please go out and play my PS2 picks, they are all phenomenal. Happy gaming.