Just checked the transmissions.

Automatic:
It looks like the European X5s got Getrag transmissions (A5S 390R - YZ) while the American X5s got some other brand (GA6HP26Z). Europe also got a different torque converter.

Manual:
It looks like both European and American X5s got Getrag manual transmissions. They are different, but not very. I'll have to check with Getrag on this.

American: GS6X37BZ - THEE & GS6X37BZ - THEX (RealOEM lists these as "GS6X37BZ/DZ" just like the DZ designation for the European models - likely, then, it's the "37" vs. the "53" that is the difference; could it be gear ratios? Strength? Who knows).
European: GS6X53DZ - THGE & GS6X53DZ - TJGB

Two problems: 1)none of these parts are labeled "For Vehicles with Increased Tow Capacity" so I don't know whether these parts were different on those vehicles and 2) I've got more questions now that I did before. Therefore, this was basically a useless exercise. What I need to do is talk to BMW and get precise part numbers.