Hi there. My son was faced with the same decision. Both schools are academically strong. Based on my own personal view, I would say that Choate has a stronger science/STEM program, and Lville is stronger for humanities. My son graduated from Lville in 2018.
Saturday classes are good to keep kids focused, but it does leave them well prepared for college. Saturday classes can be a problem if your child is an athlete and needs to compete on the weekends.
My son’s first year of college was a breeze compared to his time at Lville. I imagine the rigor at Choate is similar. Both are well regarded by the college admissions staff.
I agree with what everyone is saying above regarding college placements, especially @cinnamon1212. In the Lville class of 2018, there were probably at least 15 kids who matriculated to Princeton. Most of these were fac-brats, legacy, URM or athletes. But there were a substantial portion who were not. My guess is that if your child graduates in the top 5% from either school, they will have a good shot at ivies.
But don’t let college placements be the main guiding force for choosing a high school. Choose where your child will thrive and feel most comfortable. The two schools are more similar than they are different. We chose Lville because it was much closer to home. No wrong choice here.