I mean, you had the right idea. If you want to do MASSIVE damage on a crit, then a half-orc/barbarian with a greataxe is your best bet (Do Savage Attack and Brutal Critical stack??? 4d12 damage!!?!)
Doing completely unnecessary math, if you have Savage Attack OR Brutal Crit, then a greataxe will do more expected damage if you hit on a 15+ due to the increased crit damage. Otherwise, a greatsword is better
If you have both (or Brutal Crit at level 13) for 2 additional weapon dice, then greataxe is better than greatsword if you hit on a 9+
If you can add 3 additional weapon dice, then greataxe is better than a greatsword if you hit on a 3+
If you can add 4 additional weapon dice, then greataxe is strictly superior.