You don't want to tie the rope around a buck's neck if you plan to mount it. It messes with the hair. If you hang a buck by the head, use the rack. If you're not planning a mount, it makes no difference for hanging. Deer do drain better hung head high.

In warmer weather it is helpful to hang from the hocks, so you can pack ice in the deer. The ribs will hold the ice in. You want to make sure the melt water can drain though.

For skinning, it is best to hang by the hocks, but you want to be careful of the rack if you plan to save it. I've seen plenty of chipped tines that were caused by smacking against a hard floor.