My 104k vi has a much larger bore than a modern Selmer. In fact a bit larger than my 81k vi. My 228k Selmer has the same bore as a modern Selmer, however; I actually use a high-copper series iii neck on it (which I originally bought and used on a series ii horn).
As Simon notes, the series iii neck shape is right within the range of variability of all of the vi necks I have owned, but that series ii neck is quite different.