Quint probably stomps to be honest. Even Selene only managed to beat him by exploiting his healing and trapping a silver grenade inside his body.
They have pretty similar strength levels, based on feats, both being able to relatively casually move cars about:
Problem is Quint has nigh-instant regeneration and claws that can casually slice through elevator cables. Every swipe is going to leave a bloody wound whereas Joe would basically need to perform some kind of one-shot decapitation or something to realistically stand a chance. And Joe himself got KO'd from falling off a ferris wheel:
And, of course, we've actually seen Quint tear through superhuman vampires and such. I just don't see how Joe doesn't get shredded here.
After reviewing both, Quint definitely wins. He's smarter than Joe, faster, stronger, tougher, far more vicious, has a healing factor so fast he got stabbed in the brain and was just fine, and Selene used it to her advantage to plant a silver grenade in his stomach. Plus he has fangs and claws that are essentially swords with how big he is.
And on the topic of strength, he's so much stronger than Joe it's not even funny. We see Joe move a small car with people in it a few feet. We see Quint toss cars like he's chest passing a basketball and swat them out of his way with one hand like they're weightless.
In all likelihood Joe like Vault said, gets shredded, because Quint is bigger than him, and can heal any blunt force trauma Joe causes while at the same time tearing him to pieces and Joe can't heal from any of that.