Private Day vs Test Public Boston Area

My son has the option to attend BLS or BB&N or Belmont Hill and we are trying to decide. Financially, it’s all the same, he has a full ride scholarship from a foundation that will support him at BB&N or BH. BH is probably not an option for us because the commute would be brutal.
DS is a good student, motivated, wants to go to an Ivy League. He’s a laid back guy socially and has visited both schools and loves the vibe in both, more diversity at BLS, more buzz at BB&N. Academically, BB&N would give him more language choices but BLS has some fantastic and very diverse clubs/extracurriculars. Sports: Both schools have equally good sports team in ‘his’ sport. BB&N has longer school days (?good, ?bad), and I tend to like the shorter school days, but it also tends to have longer summers which is nice in high school.
So what would you say? He is very concerned about chances at Ivy, so, all other things being equal, would love a school that would increase his chances of the Ivys. Any advice or BTDT

All things equal, I would go with BLS over BB&N. Depends on the Ivy though. And Really depends on the kid. If you think he’s a kid who would benefit from teacher connections then BB&N is the way to go. If you think that diversity is something he needs/wants and can utilize than that can be another factor. Remember, BLS is still a public school so there are not going to be as many luxuries (guidance for one). But he might gain the advantage as there are few public schools that match BLS and it has been around for a long time. In either case, he’ll have to be top 10% or Div I,II in the sport to be Ivy league material. It’s more likely (statistically) he’ll be in the next tier in which case you might to think that through. If his scores are 99% and he is one of the best players in town then either will work. If he scored 85% and he is a strong athlete then he might gain from BB&N connections. If he is top academically and less sports than I’d go with BLS. Remember there are kids at both schools who are really excellent (top 1%) in areas. So he’ll be competing with a much different set of kids than other schools.