I think a part of it depends on when the white coat ceremony takes place. Some schools have their white coat ceremony during orientation, before you and your classmates have gotten much of a chance to know each other, so when your name is called and you walk the stage to get cloaked, you feel like you're in this alone. You get the white coat, congrats, you're in med school.
My white coat ceremony took place over a month after school started (not sure why), which was fine by me. By then my class knew each other pretty well, and I liked watching everyone receive their white coats knowing that we were going down the same road together for the next four years. Of course...one downside was that we had gross anatomy shortly before the ceremony (with an hour or two in between to shower and change), and when we were all lined up in the auditorium with our white coats, there was still the faintest traces of cadaver in the air
But hey, that made our ceremony all the more memorable