In New York, that is the only way to legally hunt during modern firearm season in most of the state. I've killed dozens of whitetails with 12, 16 and 20 GA slugs. We normally shoot them through a shorter slug barrell with open rifle sights on them. They have become more accurate over the years since most manufacturers offer a slug that has rifling grooves cast right into the lead slug. With a 2 3/4 inch 12 GA and good shells, I have an effective range (consistently inside a pie plate)of about 80 yards and I am by no means a great shot. I imagine the 3 1/2 inch guns extend that some.
A well placed shot will not ruin any good meat. I killed a buck at 60 yards last year that ran about 20 yards. He was shot in the chest just above the heart for a double lung shot. The entrance hole was about 1 inch in diameter and the exit hole, after blasting thorugh both rib cages, was about 2 inches in diameter. The slog was still in one piece, but was flattened and much wider than it was when it entered. A shoulder shot can sometimes get messy if the slug fragments. My opinion is that shooting a deer with a slug vs. buck shot is similar to shooting a rabbit with a .22 vs. shotgun shot.
On average, the buckshot is going to damage more meat because the shot does have a spread. Your range with a slug will be better as well. If shots aren't well placed, then it doesn't matter what weapon or ammunition you choose. You will damage meat and you will risk losing the animal.
My weapon of choice in thick cover where your shots will be at close range would definitely be a slug shotgun with open sights. I'd also consider using this setup when I'm hunting in an area where I am concerned about a bullet traveling a mile or more.
-lobo
P.S. My Dad's nickname is Slug and he sure has earned it. He worked for Ithaca Gun making Deerslayer shotguns and has slayed a few in his time, helping the New York State wildlife managers control that abundant whitetail herd.