Here's the differences in the two generations- in order of importance:

1. 2nd gen has an internal speaker, the first does not (any sound must be heard through headphones)
2. 2nd gen model has buttons on the side like the iPhone does for volume
3. Slightly longer battery life between charges (6 hours of video)
   
4. 2nd gen model comes free with more updated software that allows for downloading many free and paid custom applications built for the iPhone and iPod Touch.  You can upgrade the 1st Gen version to this ability by paying $10 through iTunes.
5. The 2nd gen model is a bit snappier when browsing the web - I estimate it has a slightly faster processor for handling graphics/etc.
   

The 2nd gen iPod Touch form factor is exactly like an iPhone 3G.  The only things it lacks are the phone, camera and GPS (although it can use a wi-fi internet location feature to tell where you're at if you are connected.)  The first generation model is flatter and just slightly thicker, but is still a great device.

Thanks, please rate my guide.