A 2d6 may sound better generally, but a 1d12 could be better for criticals.
Only for barbarians brutal critical, this is why I made the barbarian link regarding greataxe specifically, although i didn't really explain it fully.
2d6 and 1d12 both have the same maximum potential damage of 12, which would be 24 on a crit, the difference is in the minimum potential damage, 2d6 has a minimum of 2, but 1d12 has a minimum of 1. It's really not a lot.
But, bring in brutal critical at level 9 from barbarian, and suddenly you're rolling 3d12 for a crit with a battleaxe, and 5d6 for a crit with a greatsword/maul, here's where greataxe wins, because you're not rolling weapon damage three times, you're specifically rolling one extra weapon damage dice (see
Sage Advice for confirmation). Again, it's really not that much extra damage (at least until level 13), but when you have a community full of powergamers and damage optimisers, they put a lot of weight on extra numbers, and it give barbs an excuse to crit fish.
