The only real difference is that the GXP has a reducing insert on the left side. A GXP crank will fit into a Shimano BB, but will never tighten properly. A Shimano crank won't fit all the way into a GXP BB unless the insert is pressed out. Then it works fine.
Ah, that makes sense. See, I had noticed that the parts were different brands, but I figured that because the cranks just had to press up against the bearings, there would be little difference between the different brands. As you point out, the insert makes the whole difference, and its absence prevented the crank from tightening in the Shimano BB.