The game's PSP origins are almost invisible in this PS2 version. You might not notice it if you don't put them side-by-side, but there are countless small graphical upgrades from the PSP version. It's smoother, too, with very little of the blurriness from the portable predecessor. It also supports widescreen displays, though that isn't written on the box. And though this isn't as pretty as the latest full-sized console GTA game (San Andreas) was, Liberty City still looks miles better here than it did in GTA III.
Gameplay, too, is big improvement on GTA III, though admittedly not as ambitious as San Andreas. You can't swim or work out to change your physique. But you can change outfits (sometimes you have to get a certain job), and there are boats and motorcycles, which weren't around before. Plus, you can move the camera with your controller's right analog stick now, a huge advantage over the PSP version.
The missions themselves often seem shorter, tailored more toward the portable experience. But many players will consider this a boon, and the game still contains dozens, if not hundreds of hours of gameplay.
Multiplayer is gone - which is a bummer. Rockstar's explanation is that it wants the first GTA multiplayer on consoles to be a bigger, bolder, badder thing than the PSP game's diversions, and we get that. It would have been a nice appetizer, though.