1 Jan I believe, at least in the morning it will be like an A-Bomb has fallen in the city. Nobody in the streets, all closed... except for the discos, where you'll see people coming back home early in the morning.
Day 6 is completely different, because it's the Three Wise Man adoration of child Jesus, so there is a parade and the streets will be crowded with children and parents. Expect serious traffic problems that day. Commerces will be mostly closed, except for some gift shops and few more.
In both you could have some problems to find restaurants or even snack-bars open.