Rocky is correct. The diameters are the same and depths are different. The Euro neck is taller than the US neck. I just measured the depth of two different US tanks and they 3/4" deep. I am guessing that the Euro neck is between 1/8" and 3/16" taller.
Since the correct fitting Euro pressure caps are essentially unavailable in the US, an easy workaround is to use a higher pressure cap. Maybe use a 24 pound cap instead of 16.
Also, I added some holes in the modified cap for the overflow tank to help insure it does not act a pressure cap.