The main difference is speed, DG834GT supports 108Mbps while DG834G supports 54Mbps.
DG834GT click here
DG834G click here
Personally I'd prefer the wireless card because of the connection method, the card goes all the way into the laptop body mostly at the side while only the tip of the USB adaptor goes into the USB port.
Problem arises if the USB port situates at the back and you're surfing in bed with knees up. The adaptor will get in the way and get bent, this is personal experience, other people may think otherwise.