As one of the people here who has done such a thing; I would not worry as much about the difference. While the 1d12 vs 2d6 thing sort of annoys me in that the latter does seem better in most cases (though the more iconic combinations do come closer than I expected due to...stuff.), so far it has not seemed as that big of a deal. I'm curious to see what changes they've made in the final PH and how it affects this.
Spoiler Alert: The orcs destroyed them all.

Bounded accuracy makes low level enemies terrifying once you get a certain amount.
Darned Orcs. I hate those guys!! Kill'em all!
Thanks for the reassurances Cy, you're a trooper. I'm hopeful the devs actually do know that they're doing here and make fighting styles make up the difference or make greataxes not feel so lackluster. I really don't like rolling a 1 on a d12 crit, feels bad when I could have gotten a 2 but probably closer to a six, times two, which is often plenty good enough to finish off an enemy. Crits should be big fireworks, it never sat well with me in 2nd edition when I rolled a 1 for damage on a natural 1 and the final damage was a 2. Very disappointing. Ooooh, it's such a critical, can't even kill a kobold with that attack. Don't think it's good design to allow crits to feel like whiffs, it's confusing and contradictory and frustrating.
At least in 4th edition the base crit damage was maxed, which would at least somewhat equalize the difference between a 1d12 and a 2d6 weapon.
I'm trying to remember if 2d6 was the value for greatswords from 3rd edition, or if it was just turned into that in Pathfinder. I believe Pathfinder is where that change was made, and for ill. I had a greataxe wielding barbarian in a Pathfinder game once and he upgraded to a silver greatsword the first chance he got, and never looked back. Too bad, it would have been fun to keep the axe, but I want the biggest baddest weapon, both in character and out of character, and greataxe isn't it. This just "soft encourages" everyone towards greatswords or mauls, for no good reason.
It would have been much better to have the base damage be 1d12 across the board, except for specialists, who can get either damage advantage or damage re-rolls on 1s and maybe 2s. Let the specialists get that really good and realiable damage, and random guys using those weapons don't get to deal minimum 5 damage on every hit that just by walking into a shop and buying a greatsword instead of a greataxe.
This will all be okay in the end if there is some kind of damage rerolling mechanic for low damage rolls. Maybe that's what they did, I hope so.