All four devices are physically identical with only the carrier branding at the back differentiating them. However the Verizon, AT&T and Sprint variants of the Galaxy S III will include LTE connectivity while the T-Mobile version will have to do without.
Check out the following video review of the AT&T and Sprint variants of the Galaxy S III which compares the two devices.
Both devices run Android 4.0.4 Ice Cream Sandwich with Samsung’s latest version of TouchWiz UI on top, the software experience is very similar between the devices with the carrier specific apps being the only main differentiator
You can learn more about the U.S. variants of the Samsung Galaxy S III on PhoneArena.