By the ceremony of a bris milah there are many "kibbudim" or honors that are given to those that are present.
Here is the list (please edit and add if I missed any):
Kvater - a man and woman who bring the baby into the room (usually passing from the woman to the man.)
One or more individuals might be called out to then hold the baby before the next part.
One who places the baby on the chair of Eliyahu
The one who picks up the baby from the chair of Eliyahu and gives the baby to the father
The Sandek who holds the baby during the bris
The one who takes the baby from the Sandek to give to the next person
The one who holds the baby when the brachos are being recited
The one who recites the brachas and says the babies name (usually the same person. I've seen this split up before though.)
There is of course the mohel!
And the father of the baby!
Out of all these people who generally has the custom to put on a tallis gadol? Sometimes you'll see by a bris that people will make sure most of these people are wearing a tallis while for others there might be less of a concern that they should wear.