It seems, OP, that you might need to clarify what you mean by celebrate, or focus your question on one tradition. I hate to add more anecdotal evidence, but in the Lutheran tradition we usually hold a Christmas Eve service, one that is more attended than the Christmas day one, if it's even held.

The Catholic (or at least the monastic) liturgical day traditionally follows Jewish reckoning, i.e. the day begins at sundown, so the vigils on Christmas Eve are actually on the same "day" as the ones the next morning. This may be relevant to your question, but I'd need you to clarify.