When we had Santa gifts, they were never wrapped, so the girls had those first off, before we were up. The stockings were also free for all. However, when everyone is up and opening presents, we pass them out one at a time. We enjoy seeing what each other gets and seeing their reaction. Now, at my inlaws it's another story. When the girls were little, we went to their house Christmas Eve (that's when they opened presents) and it was mayhem, over in minutes and I had no idea who gave what to whom. It was very stressful for me. That was when Stephen and I decided to make it a little more respectful when we started making our own family traditions. It kind of makes us more appreciative of what is given.
But, all families are different. I guess a lot of it is what you're used to, and what you're comfortable with. I think one at a time presents at my inlaws would be weird.