I may have poorly stated what exactly my averages were. They were average damage including critical hits, not average critical hits.
So, the greatsword is average 7 + (7 x 10%), while the greataxe is 6.5 + (13 x 5%).
So, to take your 20 strength character does an average of 15.4 with a greatsword, and the greataxe 14.85.
Of course, a complete analysis would off the best picture, but I imagine the greatsword will edge out the greataxe in average damage at every hit probability, except for of course when a natural 20 is the only way to succesfully hit. Of course, if that happens, you probably in deep anyway.
Also, though it may not come up often, a greatsword is a vastly superior vorpal weapon to a greataxe.