In normal DnD rules, if you crit, you had one weapon damage die. So a greataxe does 2d12 on crit, while a greatsword does 3d6 (confirm by Sage Advice, but I don't know how it is coded in this game). So a class like the barbarian, who can add extra dice to a crit, will want a greataxe.
But if you exclude crit, I guess a greatsword would be more consistent.
This is partially incorrect. https://www.dndbeyond.com/sources/basic-rules/combat#DamageRolls
says "Roll all of the attack's damage dice twice and add them together"
Critical hits double ALL the weapon dice, not just one of.
Half-Orc/Barbarian's brutal deal an additional
weapon damage dice.
-A greataxe will do 3d12 (2d12 for crit + 1d12 for brutal crit)
-A greatsword will do 5d6 (4d6 for crit + 1d6 for brutal crit)