It's more of a family by family thing in the USA.

In my family, Christmas Dinner was a clan affair with maybe 20-30 gathering for Dinner. Not so much now that the grand parents are gone. They were the tie that bound every one together.

If travel was distant, and we had to leave early, all presents were opened on the Eve.
If just across town, one present was opened on the eve.
Now days, the Dinner is a smaller affair, no travel at all, presents are opened on the day.

I will say that when kids are involved, opening on the day is an excellent incentive for them to get up early.