My past experiences have been mostly art museums - we have so many of them in NYC. The only place I can recall visiting art galleries was in New Mexico. Many of them in Santa Fe and Taos have more than just paintings. They have garden statues and many have beautiful fountains for outdoors.
I choose them both. I go to museums to enjoy looking at artistic works and renderings. Also, there is much to be learned through time spent in a museum of any type. I go to galleries when I particularly want to see an individual's displayed pieces and perhaps make a purchase. Displays of local artists are an interesting way to learn about their locale.
Art museums and art galleries are few and far between around here. Any opportunity I may get I would spend time in one. You don't have to be "shopping" to enjoy a gallery, your can enjoy it the same as a museum.