@ImDictatorBowDown: Damn it! that sure is what happened...But I don't think shes hitting him with a mero mero beam, for he has soru and has haki to defend against her stone attacks via touch. My opinion tho
Hancock wins this mid difficulty ( high difficulty at the very worst ).
I don't know if she can be compared with Sanji in terms of physical strength now ( since they both mostly fight using their legs... ) but even though she might not be physically strong enough to break Vergo's defences, her DF still allows her to turn Vergo into stone while kicking him. She managed to break a Pacifista's head effortlessly and I don't think Vergo is way harder than it so it wouldn't be that much of a problem to pass through his Tekkai... ( his haki won't nullify the effect of her attacks, just the force of the blow itself, I think ). That's how dangerous her Devil Fruit is... it doesn't seem to care about barriers or anything really hard ( except for giant walls or something of important height which a slight part of them could just be turned into stone, I guess... ).
She has all 3 forms of haki as well, it's not necessarily needed in a fight but it still remains useful there. Hancock is enough prominent at it to give a lot of trouble and while it seems that Vergo has a lot of experience, I doubt he's as qualified as her in that field. She has also more than decent speed ( she's a kind of martial artist after all and mostly fights with her legs, apart from a slim and athletic body... ), her techniques could do serious damages to Vergo ( though I doubt Mero Mero Mellow or Pistol Kiss would be of use... ).
However, she hasn't displayed any kind of durability ( but I doubt she's not durable either, we are in a Shounen manga after all... ) and as Vergo has tremendous physical strength ( his bamboo stick was enough to destroy Law, and he wasn't even using his full power against Sanji... )... well, she would suffer ( her CoA won't help her each time he'll try to land a hit on her ).
In a nutshell, she would win quite comfortably but shouldn't underestimate him, especially when we haven't seen him being really serious with his full body haki as he got one shotted by the haxed law.