I wouldn't even say they are comparable... they might do a few similar things but are such completely different pieces of electronics that it's almost like saying " a computer or a television? "
My ipod touch is probably my favorite techie thing I own (other then my macbook) being that I can surf the web, read my email, us a ton of different apps from simple games to shopping lists to you name it, plus watch movies, listen to music, store videos/photos etc etc etc... hands down a wonderful purchase and I couldn't recommend anything more.
That said the Dsi I is also great, but it's main purpose is for playing games... much more detailed games then any little application you'll have on your ipod touch.
So... if you're looking for a game player get the DSi, if you're looking for something else get the ipod touch.
The iPod touch is definitely the better choice. The DSi is new and nice, but the Touch has much more functionality. With the amount of apps on the app store, you will never get bored, and is definitely much better than the DSiWare shop. I've had a touch for 18 months now, and i have gotten the most use out of this device than almost and device I've ever owned. The internet based abilities are WAY better than anything the DSi has to offer, with a built in Mail app, Weather app, Stocks app, Google Maps app, not to mention a full web browser that is easy and intuitive to use. And by the rate that it is progressing, it will only get better in time. I bought mine when it came with 13 apps, including music photos, videos, safari, you tube, but now, it has over 100 apps that i use almost on a daily basis. Many of the games lately have been pretty crappy, but older and more expensive games (9.99 for an iPod game vs 19.99 for a DS game) have much better replay value, such as some of the racing games, or Rolando. Plus, even as a 15 year old, i use a simple finance application to track my daily spending and earnings.
Bottom line, the ipod touch provides way better value.
I say it depends on your needs. I have an iPod Touch and I love it. You can play games on it, listen to music, and use a lot of PDA-like apps that are web-compatible. If you only want a gaming device then the DSi is probably a better choice since that's what it's made for. If you mostly want a media player, PDA, or Internet browser then the iPod is definitely a better choice. It really comes down to priorities. Choose which is important and go with the corresponding device. They both crossover into each other's territory, but they are both better at what they were originally made to do.
The Itouch doesn't have a camera. I love my IPhone and all the camera apps plus the games and online games. I use it everyday. I want the DSI but not as badly. If you trade in your DS lite at Gamestop you get $70 off the DSI but I am waiting for pink.