Combat modifiers are arcane and bizarre in how they work, and they can depend on whether a unit attacks or is attacked to boot. Combat 1 on a Vulture fighting an Axe makes a comically large difference, especially compared to an Axe in the same situation. Assuming no defensive terrain/fortification bonus/river crossing/other shenanigans:
C1 Axe vs. Axe: 68.1% | C1 Vulture vs. Axe: 65.7%
C1 Axe vs. Sword: 79.7% | C1 Vulture vs. Sword: 79.7%
C2 Shock Axe vs. Axe: 90.1% | C1 C2 Shock Vulture vs. Axe: 88.9%
C2 Shock Axe vs. Sword: 96.8% | C1 C2 Shock Vulture vs. Sword: 97.1%
C2 Shock Axe vs. C1 Shock Axe: 67.6% | C2 Shock Vulture vs. C1 Shock Axe: 66.4%
C2 Shock Axe vs. C1 Shock Sword: 88% | C2 Shock Vulture vs. C1 Shock Sword: 80%
The point to take from this is that compared to axes a Vulture really shines against non-melee units, and against melee units you really want to build a Barracks first. For example:
Archer fully fortified in a flatland, 0% cultural defence city: CR1 Axe 61%; CR1 Vulture 71.8% | CR2 Axe 71.3%; CR2 Vulture 88.4%
CG2, Drill 1 Archer in the same situation: CR1 Axe 19.4%; CR1 Vulture 39.8% | CR2 Axe 24%; CR2 Vulture 61.7%
CG2, Drill 1 Archer fully fortified in a 40% cultural defence hill city: CR2 Axe 2.5%; CR2 Vulture 15.3%
C1 Horse Archer: C1 Axe 27.2%; C1 Vulture 50%