Wolverine even with a healing factor, gets hurt, knocked out, pinned down; Cage is more than able to do all three to him.
Wolverine can't instantly kill Cage, no matter what people may think.
Cage is also a dang good fighter. He was good before training with Iron Fist. He's taken powerful explosive blasts unphased, he's fought Hulk, Wonder Man, Ironman, Iron Clad. His strength's not an issue here.
Durability is, and Wolverine is not just going to slash him like a regular human.
Wolverine's had some great fights against Hulk, but Cage is a much cannier fighter.
Hulk fights a lot like Wolverine himself. Taking massive damage to deliver a hit. Wolverine's a fairly skilled fighter, but usually just brawls. Cage can get wins here.
Does Cage really have an allergic reaction to adamantium, or was that just canon for the game? If he is, I don't see how in the world Wolverine would lose this. However I have not been keeping up with him lately so I don't even know if he still has an adamantium skeleton, or if he got his HF back. I don't know how Marvel allows it's writers to go buck wild on their best characters?