If it comes right down to it, I would go with a map, and neither compass nor GPS - in mountainous terrain. I can think of just one occasion where I used my compass in the mountains in good weather - that was forty years ago. My compass tags along because my compass is also my signal mirror when I am in recreational mode.

Realistically, if you are hiking in familiar terrain, you might be able to go without anything, but I really like to have a map - a good map - appropriate scale with accurate contours.