We were forced to hunt with slug guns for years in NY, and IMO a shotgun is about as lousy as it gets for a deer gun, they kick like heck, are very expensive to shoot, and are innaccurate with $2 a round ammo as well.
Muzzleloader is the only way to go, they are so much more pleasent to shoot, and actually supprisingly accurate. I've got a T/C Omege Stainless that I bought for special ML season, and I occasionally take it out durring rifle, and believe it or not, I do not feel handicapped by it.