The reason I say Wolverine gets the endurance edge is because essentially any character that has a healing factor has shown that it can get over-taxed (except maybe the Hulk, but that also escalates with his rage). Wolverine has shown that his can be over taxed, or over strained, if needed to continually heal from long, sustained punishment. This might be a little bit of ABC logic, but I think the same principle would apply to Green Goblin.
So, what I am saying, is that Wolverine, blow for blow, is likely to take less damage and therefore less healing taxation than Green Goblin. Not only do to his incredibly high healing factor, but due to his adamantium skeleton which will reduce blunt force impact. The real taxing on Wolverine will come from Goblin's fire attacks. But, how likely is Osbourne to sit at a distance and do the entire fight at range like Iron Man and blast Wolverine to bits? I don't think that's very in character. Osbourne is smart, but he revels in overpowering his enemies as well.
On the flip side, even if he were to realize that's his only hope and were to do so, how likely is Wolverine to stand there and let him? Wolverine has experienced combat for over 100 years, he's going to dodge, cover, and hide. Then maneuver under cover where Goblin can't see him to close the distance again. And if he can't, certainly at some point such an energy exertion (like I said this fight could go for days) would tax Goblin's endurance. Even as a Super Saiyan, repeated Kamehameha's will wear down Goku (different Universe, different rules I know, but I think the point is valid).
If Goblin takes to range, and stays at range, I say it's a stalemate. I don't think Wolverine would stay on the street and let Goblin blast him. Take the fight to the subways were Goblin can't use his insane leaping and maintain distance. But you could argument Goblin would be too smart to follow. So if this becomes an attempt at a range fight, stalemate. If it mostly stays up close, Wolverine (barely) after a several long, bloody days. But even then Goblin still has the chance to win even up close, I just see slightly more wins in Wolverine's favor.
You do realize Wolverine will be taking A LOT of fire damage as well?
Yes, I included that bit as well. The fire is Goblins biggest/only severe threat in this. Fire vs healing and claws vs healing. If Goblin this Wolverine with a strong enough and well timed fire blast, I honestly think he can KO Wolverine in one hit. I'm not disregarding it.
If Goblin melts off Wolverine flesh, that requires a lot more healing than a slice. A slice heals fairly quickly due to skin just having to be healing in a space less than an inch in width. A full on melted body requires nearly every cell to be replicated. By your argument of taxation of Healing factors, Wolverine has a disadvantage.