Completely not an expert on this one. I'm sure someone more helpful will be along shortly. The most obvious of the pros are:
a) Children are never left alone in the dormitories during the weekends.
b) Boarders have everything scheduled to fit in with their routine, nobody is worrying about weekly/flexi/day boarders.
c) Everyone is in the same boat- no jealousy over X going home on Friday, or Y getting to stay for the weekend activity.
d) Most full boarding schools have been around a while and know their business, otherwise they wouldn't survive providing something that isn't the default education it once was (for some families, obviously full boarding has never been the default for most children). Anyway, this means they are some of the top schools around. They know exactly what they're doing.
Cons:
a) if your situation changes, and you want your DS to spend more time at home, then obviously you have to choose between that and their school.
b) Hard to take the occasional time off, e.g. a weekend out. This is the trade off for not being left alone in the dorms.