I have both a "Fat" 3G version and a "Slim" (only WiFi), Here's my comparison of both:
PROS
10XX models (Fat)
-Have an OLED Screen, colors look more sharp and bright.
-There's a 3G&WiFi version that you can use as a smartphone (kinda). Legally is only for AT&T, but can be circumvented.
20XX models (Slim)
-Charge cable is a typical microUSB, so it can be replaced easily.
-Its less heavy.
-Battery life is longer.
CONS
10XX models (Fat)
-Is kinda heavy, and long playing sessions can get you hands a bit tired.
-The charger cable is a proprietary one and they're not easy to find/replace.
20XX models (Slim)
-Screen is less sharp and colors not that well defined, some say that black color looks grayish.
There might be other facts that I've missed, but this should give you an idea of which one to get.