I think Wolverine could do some superficial damage with the claws. A pretty blatant Wolverine homage had no problem opening Superman's chest up with his claws in For Tomorrow, for one.
As with 99% of things though it does vary from showing to showing; I've also seen Superman get batted into space by a magical axe and no blood was drawn, only his costume was damaged.
I don't think he would ever do more than superficial damage though, so either way no, he can't win. Even if Superman slugged it out without using his flight or speed he would win.
Equus was a magically-, chemically-, electrically-, and cybernetically-enhanced OMAC with claws forged from angelic flesh. He wasn't a Wolverine homage in any way, then, I don't think. If anything, he was more akin to Doomsday. Regardless, his powers and power sources make him nothing like Wolverine, so, in my opinion, your comparison is off.