@Center, I asked my daughter the question you posed. She attended a well regarded LPS before transferring to PAA. As far as total time completing homework, she indicated there was a nominal difference. She took 6 courses per semester in public school and 6 course in private school–both of which demanded decent time management. The key distinction she found was that at PAA she needed to become a better writer, and thus, spent more time trying to apply critical thinking and clarity of thought to her essays. (BTW, thank God for that!!! Our LPS was not strong in developing writing skills, and that was the single biggest factor in our sending her away to pursue a “better” education.)
The other factor, as several folks have mentioned, and I know you know about from your prior posts, is that she needed to be prepared to not only answer questions in class, but to develop lines of inquiry that would forward a discussion in class.
One mitigating factor…Andover believes in the holistic student. If she had more than 2 tests on the same day, she had the option–which she regularly exercised–to postpone a third or fourth test.
Hope that helps, and hope your son had a great year at PEA (despite the “obscene” homework load). 
I worked in our school district for the past few years until this past month, so I’ve seen the class schedules of your high school student first hand. Here is one of the HUGE reasons we choose BS over the LPS.
Freshmen LPS schedule:
-Algebra I
-Integrated Science
-English I
-Fine Arts elective (choice of Choir, Art, or Forensics)
-Health (1 semester) Career/Life Planning (1 semester)
-Elective
-Elective
The two electives they can choose from PE, Agriculture classes, FACS (HomeEc), Industrial Ed and a few Business classes.
Our LPS only offers Spanish I & 2 as a foreign language and it’s an online course proctored by a non-Spanish speaking teacher. They also don’t even offer a History class to Freshman! All of my friend’s children go to school here and they have on average less than 30 minutes of homework a night!
So, yes, definitely in our case the BS was crucial to her being challenged in the way she needed. The academics are by far harder and more challenging than our LPS. I think that a lot of people that live in big cities with multiple school choices around them don’t realize how many schools like the one in our town exist. I felt like my daughter wouldn’t have even received a sub-par education here.
Our D is at Hkiss and the level of depth covered in classes there is definitely fuller than we have experienced in other types of schools. She gets good grades but she has to work hard for them. I think the most significant factor in this being the reality is that all of the kids are strong and high achieving learners and they motivate one another.