Just some info for you, the 30-06, .308 and the 6.5 X 55 are all "military calibres" though with the 30-06 & 6.5mm not recently.
I have shot boar with the 6.5mm and they dropped perfectly well.
The .308 replicates approximately the same performance as the 30-06 but does so more efficiently.
The recoil from the 6.5mm is kinder than the others and in scandinavia the hunters have been using the round for over a century to take moose. It would appear that in the hands of someone competant it is adequate for significantly larger game than boar. Whichever you go with, bon chance!