The PSP definitely has more features—movies (but forget the UMD format—there’s hardly anything available), skype, an Internet browser (but it’s really clunky and no fun to use), photo viewer, etc. But it really depends on what games you prefer. The PSP is more for devoted gamers. So if you are into those sorts of games you’ll probably like the PSP more. The DS lite has a much larger selection of games, the touch screen offers a different sort of gaming experience, and you can choose puzzles, arcade-style games, role playing games, etc. The downside is that pretty much all you can do on a DS is play games. The price of the games varies. Some PSP games are really expensive and some (like Patapon) are reasonable. Most DS games are $20 and above, but you can buy both types used and that saves you a little money.
I have a DS lite and used to have a PSP slim. As it turned out, I never played with the PSP. The only game I really enjoyed on it was LocoRoco, but the others were just no fun for me (but I’m definitely not a traditional gamer). I never used it to browse the Internet, I watched maybe one movie on it, and I wound up selling it. I play on my DS almost every day. You might want to wait (if you decide on a DS) because, supposedly, they’re going to start selling the newest version (with the camera and two touch screens) starting in April in the US (just a rumor).
One other suggestion. If you’re really wanting something you can web surf with and play games, you might look into an iPhone or an iPod Touch. It’s not a true gaming device, but you’d most definitely have the best of all worlds. The Internet experience is superior, the games that are available are amazing (and far cheaper than DS or PSP games), you can watch movies and YouTube. But, it’s really expensive up front and over the long term because of the contract (if you go with the phone).
Bottom Line: If you’re a hard-core gamer: PSP. If you enjoy a variety of games and touch screen play: DS Lite. Best of both worlds: iPod Touch or iPhone.