I can't see any way Wolverine could take out Ghost Rider. The only time I've seen Ghost Rider seriously hurt was either by a magical attack (e.g., hellfire) or by some sort of technology that was specifically designed to take out magical beings. He's had his bones blown apart and re-formed almost instantly. He can also repair his bike by force of will if it's damaged. Plus his bones and bike are basically indestructible anyway.
Meanwhile, Ghost Rider is far stronger than Wolverine (I'd say he's somewhere between Spidey and the Thing in terms of strength), and he has a long-range attack (swinging his chain and sending the links flying out like bullets) whereas Wolverine doesn't. Even with Wolvie's healing factor, a barrage of unbreakable chain links piercing through his body would probably slow him down.
Plus GR has his penance stare. He looks in your eyes and makes you feel all the pain you've ever caused. Imagine what that would do to Wolverine. That's not really the sort of attack that a healing factor and unbreakable bones can defend against.
In summary: I don't really see how Wolverine can hurt Ghost Rider, and I can see a bunch of ways Ghost Rider could hurt Wolverine.
So I vote Ghost Rider.