Overall Length 3.7 in (94 mm)
Case Length 2.1 in (54 mm)
Neck Diameter .540 in (13.7 mm) (No data, but inner diameter should be the same as for .50 AE. Might be a bit thicker in the wall though)
Base Diameter .587 in (14.91 mm)
There is a huge difference in bullet weight, powder capacity and over all length.
To compare the .500 S&W lands some where between these two with a case length of 1.625 in, overall length of 2.3 in and a bullet weight of 300 - 500 gr, though I've seen up to 1000 gr loads.
All in all a 12.7x55mm can be massively more powerful than both the .50 AE and the .500 S&W Magnum.