I was recently in Buenos Aires on Christmas Eve (Nochebuena) and on Christmas Day. Most places closed early on Christmas Eve, if they were open at all, and as I recall, they were mostly still closed the following day.
If you reserve ahead of time, you can find plenty of restaurants that have a special holiday dinner for Christmas Eve, and probably some with some kind of Christmas Day meal. If you do not, they will probably be completely booked and not taking regular seating. At least, to judge from the half-dozen that I checked out.
At least on Christmas Eve, most of the grocery stores that one would normally expect to be open late are closed, but I did see that some small grocery stores were open. From talking to a few of the employees, I got the impression that these stores might have disproportionately been owned by immigrants who were not Christian or did not observe Christmas quite as strictly, so some neighborhoods with a larger foreign population might be a good place to look for shopping on Christmas Eve or Christmas Day.