I kind of stumbled onto this thread and became interested enough to do some research on the native mason bees and leafcutter bees (and in fact have now ordered a kit for the leafcutters...)
Frank, I don't believe that honeybees overwinter underground? as far as I know they spend the winter in their hives, whether those hives are manmade or of their own making in a tree or whatever (in warm enough climates). Bumblebees, and no doubt other types, do spend the winter underground, however.
As to the mason bees vs leafcutter bees - my understanding at this point is that the mason bees are more suited to an area with fruit trees that are blooming in the early spring, while the leafcutters are more suited to summer-flowering vegetable crops like cucumbers, squash and so on. They DO use plant leaves to make plugs for the tube structures where they deposit their eggs, whereas mason bees use clay or mud. So, that might well be an issue for someone growing ornamentals and not wanting the leaves to be damaged - in my case, I'm growing veggies and ornamentals, including native plants, but I don't really care if the leaves have some holes so I think the leafcutters are the ones that will work best for me.
Annie, I have to thank you for asking the original question - I've been debating for a couple of years about getting a couple of bee hives; years ago my ex and I had 10 hives and I thoroughly enjoyed that experience - but I'm a lot older now and after giving it a lot of thought have decided there are more cons than pros to going that route at this point. Giving a home to some of the native bees seems like a great compromise, since my main objective is to increase the number of pollinators in our area.