I am too busy myself, but does the 7.33 vs 7.50 account for critical hits? I guess not, but that could make up for that difference!
Ok, I did a quick research, and assuming a hit on a 10 and a crit only at natural 20, I found out, that both the greataxe with greatweapon style an the lonsword, two handed with (advanced) duelist style do an average of 4.4 damage per attack.
So actually, even though a longsword two hande with +2 damage seems better, the greataxe can still keep up.
If your hit chance is lower, the greataxe gets better, if your hit chance gets better, the longsword is ahead... by 0.0X damage per attack on average.
A champion, hitting critical at 19-20, will do more damage per attack with the greataxe.