I agree with Shadowfox. I can easily get between 4 and 8 hours use out of my PSP on a single charge. It's not too bad, seeing as if I play games on it while travelling, it's usually in bouts of about 20 minutes at a time.
The only thing I wish they'd do differently on the Vita is making games that focus on the platform's strengths. With the PSP, all the developers tried too hard to make PSP games that mirrored the PS3's games. That's why the Nintendo DS was so much better than the PSP, because its games focused on the NDS's strengths, not on trying to mimic the more powerful platform's games.
Games that actually did it right on PSP, from what I've played, were games like Patapon and Loco Roco. They felt like authentic PSP games, not dumbed down PS3 games.