On average, a greatsword will deal a basic 7 points of damage, for the axe this is 6.5. There is also the lighter weight to consider.
Critical-hitwise they are very nearly equal. Having double the threat range of the greataxe but doing half the extra damage means they are equal, with two exceptions.
The first is that the concentrated damage from the axe may enable it to strike through a damage resistance the greatsword cannot.
The second is that against enemies that require a 20 or more on your attack roll to hit for at least one of your attacks. If this is the case, rolls of 19 for those attacks will miss and you basically reach only half the effect of a critical hit. Which means that under such circumstances, your sword will lose a third of its striking power.
Considering that many enemies tough enough to make the axe the better weapon are either rare, immune to critical hits, or shouldn't even be attempted at your level, on the whole the lighter weight and greater average damage of the greatsword would gain preference over the greataxe.
However, once you start pouring feats and weapon abilities into the equation, particularly improved critical and/or possibly, you see the threat ranges improve to 17-20 or even 15-20 for the greatsword, opposed to a 19-20 or 18-20 for the greataxe.
Enemies that require more than 17 to hit on your worst attack are already much more common, even more so those who require more than 15. Which means that when comparing keen weapons plus improved critical feats, the greatsword is becoming less efficient compared to the greataxe.
Of course, you should simply go with whatever looks better (as always) rather than worrying over a few points of damage
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