of course, greataxes average 0.5 damage lower than greatswords, so greatswords are better, especially if that 0.5 is a large part of the average damage. Scythes are better than Falchions.
Another relevant thing is that dealing 4d4+10 damage to an enmy that has 14 HP left or doing 8d4+20 damage has the same result, so the scythe is better for the occasional spike damage (which happens on random targets), but the falchion is more consistent.