Battery :
Lasts anywhere from 2-8 hours. Wifi on, screen on brightest and volume on highest drain the battery a lot quicker.
Games :
Very strong. The RPG genre is more defined than on DS, has almost all the genres, with games like Mortal Kombat to Lumines to Ridge Racer and upcoming God Of War. Has plenty of ports from the PS2, and getting newer ones as well (like Manhunt 2). Good lineup for 2007.
Screen :
Its the thing the PSP sells for. I can read comics/mangas, watch videos on high resolution. The screen is brilliant. UMD movies don't sell, but each one of them looks just as good if not better than DVD on a good LCD TV.
The whole firmware stuff :
People downgrade their firmwares on the PSP to :
1. Run downloaded games.
2. Run applications like screen capture, Game Boy/Game Boy Advance/Nes/Snes/PlayStation/Saturn emulator - All of them run perfectly. The Playstation one keeps getting constant updates.
Firmwares upto 3.03 can be downgraded (but you'll need a real copy of old GTA LCS PSP game to accomplish the downgrade process). The original current firmware from Sony currently stands at 3.10.