Even with its limited power, the psp is a pretty solid portable device which we could put bewteen a PS1 and a PS2 in terms of power. Sometimes it could even be considered a portable PS2 and that's why I'm here today. To put a few examples of games where you'd had a similar experience playing on a home console and the PSP:

Manhunt 2, Silent Hill Shattered Memories, Spiderman 3, Star Wars: The Force Unleashed and The Simpsons Game: All of these games had a Wii version that was ported to the PS2 and then again ported to the PSP. In every case, the games look nice and Star Wars has extra content.

Giitaro Man Lives! and Tony Hawk's Underground 2 Remix: Both are games originally released on the PS2 running at 60 FPS that when converted to the PSP, they ran at 30 FPS but it was compensated with more content than the original versions.

Midnight Club 3 Dub Edition, Crash of the Titans and Tony Hawk's Project 8: I can't talk much about these since I've only played them for like 10 minutes. I can see that they are pretty close to the PS2 versions but you'll have to tell me if there are more (or less) features.

Also, Honorable Mentions for GTA LCS, VCS, Kingdom Hearts Birth By Sleep, the God of War games and Dante's Inferno. The GTAs and Kingdom Hearts are not exactly ports but it almost looks like they used the same engine of the PS2 games or at least they replicated those graphics pretty well. The God of War games also aren't ports but they control and feel like the first 2 games. Lastly, Dante's Inferno is impressive if you consider the original version is an Xbox 360 game but from what i've seen, it removes some content so it isn't exactly what I have in mind.

Those are all the games I can think of right now, if you have more examples, please put them in the comments!