Boarders are required to complete on average an additional two hours prep each weeknight, it is supervised to ensure they do it. They may do more if they wish. They are also expected to work hard in sport, the arts and the community and have far more expectations put on them that you would see in the traditional 9-3 school!
In boarding schools there are strict times allocated to working and the student can be punished for not working in these times. Day scholars face many distractions at home and can easily get help from their parents or siblings on these matters. Teachers at boarding schools also give more homework to their students because they know that they have to do something during these homework specific times.
In my classroom, there are 11 boarders. Out of which only 2 work hard. Only the two students want to learn and score. It's a common misconception, I personally feel, that boarders work harder than day scholars. Appears negative to me. The boarders have nothing to do but study. God knows if they study or not, but they sure as hell do not score! They show no interest in classes. They have the added advantages of extra classes, time tables, scheduled activities. None of which day scholars follow. It's just that the boarders GO to all of these classes, regardless of their interests. They just ATTEND these classes. They make NO effort to do something worthwhile. While I'm saying this, I do not mean day scholars work harder. Not all, but a handful(more than the total number of boarders, obviously) do work hard - they exhibit deep interest to learn and score - despite everything else that they do at home(differs with each person). Now I come to the point where individual effort matters. I work hard because I want to, because I'm deeply motivated to so something worthwhile in this lifetime. Not many people are mature enough to understand this nor are they motivated in any way. But I would still like to state that day scholars work harder as they have to balance their house duties and studies while boarders don't. Boarders just don't realize and use their advantages. Day scholars seek advantages.
I don't think it matters whether a student boards or not. It depends on their motivation levels of the individual student. A day student can come home, then work 5 hours straight. Similarly, a boarding student could flunk all their homework and learn nothing.
In my opinion it makes no difference whether a student boards or not.