You're missing a case of melee with bonuses, Belisar.
Eg. swordsman with C1 + Shock + 3 turns of fortify (=+15%). This would give the sword +50%.
Axe vs. sword+50% = 5/6 -> ratio 0.833
Vulture vs sword+50% = 6/7.5 -> ratio 0.800
-> axe/vulture ratio 1.04 (same as axe vs. vulture)
In most cases of vs. melee, axe is better. In some cases vulture reaches axe. This all depends on how much bonuses are applied - you just happened to pick the case that is best possible for vulture
I think with base strength of 6 Vulture would need +35% or so against melee to be exactly as good as axe in majority of cases (again fringe cases could lead to vulture being better even).
Eg. swordsman with C1 + Shock + 3 turns of fortify (=+15%). This would give the sword +50%.
Axe vs. sword+50% = 5/6 -> ratio 0.833
Vulture vs sword+50% = 6/7.5 -> ratio 0.800
-> axe/vulture ratio 1.04 (same as axe vs. vulture)
In most cases of vs. melee, axe is better. In some cases vulture reaches axe. This all depends on how much bonuses are applied - you just happened to pick the case that is best possible for vulture

I think with base strength of 6 Vulture would need +35% or so against melee to be exactly as good as axe in majority of cases (again fringe cases could lead to vulture being better even).