All the 883 Sportsters share the same engine and drivetrain. Any performance difference will be due to minor variations in weight. All the Low Sportsters have lowered suspension and seats to better suit smaller riders (women riders are a big market for Sportsters). The Iron 883 is cosmetically different (black and "tough"-looking)
The 1200 Low, Custom and Nightster use the same engine (a larger version of the 883). Otherwise they are much the same as their 883 counterparts. All are air-cooled.
The XR1200 uses a new version of the 1200 engine with hotter cams, pistons, etc to pump power up to about 100 HP. It is a new bike, with actually good handling and brakes - while no Ducati, it is a pretty reasonable bike for someone who likes to ride. Needs to be 100 lbs lighter. Gas tank is too small, also. It is air/oil-cooled. It is probably the best performing of all the Harley's (with the possible exception of the Street Rod version of the Vrod (now discontinued))