Anyways, time to type up my official vote. I believe Skull Knight wins here.
AP is not very different, unless Kary does her 3x amp. This is due to the feat Skull Knight and his shield scaling to being one that did not damage Dragonslayer, the original object of scaling. Meanwhile, the feat Omega did that gets doubled for Kary's AP wasn't a casual one. Kary was able to replicate Omega's feat much more easily, and I'm not saying she can't damage Skull Knight, but I think the rather small gap to begin with will be pretty much negligible and his shield should hold up just fine here.
Kary has better range usually, excluding Skull Knight cutting the kilometers tall guy in half, but given the speed they're moving at and that
Skull Knight's horse already doesn't like gravity and can jump super far, I do think that despite Kary generally trying to keep a distance he can close in on her. His own teleportation and better skill feats help too.
Speaking of skill, Kary's by no means unimpressive. Omega and Xero were incredible operatives even before augmentation, and post augmentation they could kill an army, their own robotic clones who had all their data despite being worse off physically, and Kary (Though obviously she doesn't scale to her own defeat) among other things. Can pull up the explanation I've typed before at some point. The thing is, Skull Knight's just better here.
- Skull Knight has opposed the God Head for a millennium, meaning that for thousands of years he has endured apostles being drawn to him constantly, especially when he tries to rest
- Even being alive means he somehow survived the original Eclipse. Keep in mind, even Guts only lived because Skull Knight saved him and Casca, and he did extremely well all things considered. Most people just got splattered immediately. To endure the Eclipse is to endure an endless tide of physically stronger abominations, each one raving to consume your soul. Zodd proves that not all apostles are bestial, and there are in fact some who themselves posses impressive combat skills.
- Speaking of him, Zodd has admitted that Skull Knight's the only non God Hand that he can't beat. Zodd has been alive and fought for centuries, and even when staying in human form was considered a pretty much hopeless fight for anyone and was called "the god of the battlefield". Zodd even conclusively beats Guts, and Guts needs the Berserker Armor to stand up to his Apostle form. SK has beat apostle zodd so many times that he doesn't even really register Zodd.
- This means SK scales above Guts. I can explain this if really needed, but it's long and expansive so I don't want to.
On the topic of abilities: Skull Knight may seem barebones (hah), but I think what he has paired with his skill should give him the win.
You can see my WIP revisions here, but I might have found him precog and definitely found Type 2 immortality. Kary's durability negation isn't something she uses, and she didn't TK ragdoll anyone important (She did it to some fodders early in the series, but never to the Cyborg duo, like her transmutation). Being a skeleton means she can't recharge off Skull Knight, and given the location she can't go nuke civilian populations to recharge either. Her AoE is a definite issue, but Skull Knight's shield, maneuverability, and Type 2 should make sure he doesn't just get blown up from afar immediately. If something puts him on the ropes, he's likely to spatial cut to teleport above her then pull out his reality breaking slash, like when he tried to assassinate Griffith. This is supported by him activating the sword in other times he would have been overwhelmed, like against those trolls. Kary's shield won't vaporize his sword. It did to so Omega's bullets and Xero's standard issue swords, but not their bodies, Xero's more exotic melee weapons, Omega's explosives (they just detonated) or his bayonet, so I don't think it's the same paygrade as her regular attacks by default. Zombies are no issue whatsoever.
So yeah. Bone man wins.