1 to 3: Toddlers lack the attention span to open a slew of gifts all at once. If you let your child open presents at the party, you might have her do it as each guest arrives. If she's opening them afterward, let her do it over the course of a day or two. (Either of these tactics help minimize or eliminate giver's regret, when young guests decide they'd rather have that gift for themselves.)
4 and up: Older kids have fewer problems with giving presents and opening them, but they may be so anxious to have theirs opened next (or, for the birthday child, to open gifts quickly) that any semblance of the spirit of giving and receiving is lost.
If your child has his heart set on opening presents at the party, turn the gift presentation into a game that slows things down and keeps it fun for the "audience." Tag each gift with a number or color as guests arrive, and have your child pull corresponding slips of paper to determine which present to open next. Or have guests hide the gifts in one room, then let him find and open them on the spot.