Yeah, I've got 2 PSPs; one PSP Go and one PSP fat.

Fat one is better as it's got a UMD drive, but the Go version has gotten a 16 GB storage. Got some games for them, like Ratchet and Clank and GTA LCS and VCS.

You can play PS1 games on both PS3 and PSP, so if you downloaded a PS1 game via PS3 you can copy it to your PSP.

Plus, there's a function called Remote Play, which allows you to remote control your PS3 via PSP using either a direct PSP-PS3 connection or internet connection. Fun feature, but not that useful. You cannot play PS3 games using that function, but you can watch youtube videos on your PSP that way, or play the music that is stored on your PS3.

Graphically wise it's awesome; basically as powerful as a PS2. The newer versions of the fat PSP even got a TV output.

Not good, it lasts about 3 hours when fully charged, with the lowest brightness level, and when you're playing a game (on the fat version), it'll last half as long.

The PSP Go battery is a bit better it would seem. It lasts for about 4 hours with the lowest brightness level, can't really judge about how it is when you play, cause I use my PSP go as a storage for music, while all my games are for the fat PSP.