I'm quite lucky having both the W123 ATE and W126 ATE brake calipers to compare. If one set had been of another make it might not be so clear.
I can confirm that
1) the brake pads are the same
2) the discs are the same
3) the brake pistons in the calipers are the same
4) the caliper mounting bolt diameters are the same but the bolts are of a different length
5) the distance between the centres of the mounting bolts are the same
6) only the thickness of the mounting side on the W123 caliper is thicker - the casting is slightly different in this area - that's it.
Here are the pictures