Not an appreciable amount, and quite a bit less considering the great axe is usable with the great weapon master feat and the long sword isn't. Yeah you would have a slight edge in minimum damage, IF there wasn't a great weapon style that let you re-roll 1's and 2's.
Great Weapon Style still leaves the greataxe behind a 2-handed longsword with +2 damage.
Longsword (Versatile, Dueling): 1d10+2 = 7.5 average damage
Greataxe (Great Weapon Style): 1d12 (rerolling 1-2s) = 7.33 average damage
I allow the dueling style to apply to versatile weapons. Check with your DM. My reasoning is that they could be using a shield so giving up 2AC to have an extra hand on the weapon isn't a big deal.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.