It definitely varies. As far as I know, it varies in 2 ways: some characters deal more damage with their counter animation, and their animation can affect whether or not the hit hits the enemy's head.
Chris is the most powerful character when it comes to counters. I'm not completely sure, but I think he can counter kill every enemy in catacombs without hurting them first.
Yeah this is correct. On certain stages enemies seem to have different health as well. Female zombies also seem to have less health than males.
For example, the zombies in urban chaos predominantly do the arm swing melee -
with power counter, everyone holding a
2 handed weapon gets an instant kill, most holding a 1 handed weapon cannot, except with the females.
without power counter, Chris holding a 1 handed only gets kills on the females.
In mining the depths, the zombies do the overhead grab melee -
with power counter, everyone holding a
1 handed weapon gets and instant kill and vice versa.
without power counter, some characters holding a 1 handed also get instant kills (Chris and Ada in particular)