For every time the axe user kills that 10 HP monster one round sooner due to the swinginess of a single damage roll instead of two, there is another time where he rolls a 1 or a 2 and fails to do so. It can take a lot of rounds worth of actual hits before your actual damage converges to your expected damage, and rolling more than 7 on a d12 when you have a +3 strength bonus results in overkill anyway.
So, anyway you slice it, the greatsword wins. The only question you can answer is how many rounds does it take you to kill a foe? Being able to have a 70% certainty of killing it in three rounds vs a 40% certainty (or whatever the actual number is), makes the greatsword or maul much more reliable. This combined with the greater minimum and greater average damage, makes it a far better weapon. Reliable damage is worth a lot.
If the crit rules are now double damage, the opportunity cost for rolling low with a greataxe is doubled compared to a greatsword, and overkill becomes twice as much an issue. Rolling 2d6 + mods x2 is a lot closer to an average value than 1d12 + mods x2. Every point of overkill from the greataxe is simply wasted damage, and doesn't result in the enemy dying any rounds sooner.
Either all three should be 2d6 or all three should be 1d12.