Size, weight are the biggest, but the G1 is no longer in production. There are really no accessories for it and right now they are only supporting it in term of fixing bugs, but no new features.
The G2 is smaller, has additional accessories, including a home dock, right now it is getting all the attention by development in terms of bug fixes, added features and improvements.
The G2 in my opinion having both is much more stable, much more user friendly. Battery life is better and the feature set is better. Two big things for many the volume normalization so you don't have louder and lower volume songs during playback. Plus there are equalizer settings. Various backlight settings and even a large text overlay for using it in your vehicle.
The G2 cost more right now because it is the primary portable, but the G1 can be found on Ebay and at various online retailers at really good prices.
In my opinion though, I'd skip the G1 and go with the G2
This answers a question that I had. I have noticed when listening to the web player that the songs were not normalized and I was wondering if I would have the same problem on the G2. Good to know that I won't have to keep my hand on the volume control for my car stereo.