I think the big difference here is in size. Middlesex is ~400 students. Loomis is more than 700. I think your daughter may want to give some thought as to which environment better suits her. I am more familiar with Loomis, so here are some comments:
Pros: Loomis has a brand new theater/dance facility that is opening up this week - they are doing Spamalot for their musical. Loomis also has a well regarded writing program that takes place sophomore year (similar to MX). The town of Windsor is walkable from campus (grocery store, etc.). And the campus has a wonderful feel to it, with a good amount of new buildings and new dorms. School leadership is solid (although see comment below) and the admissions department is strong/responsive across the board. The school is very close to Hartford’s airport if you are boarding from farther away.
Cons: The Head of School at LC is transitioning away in June 2023, so like MX there is some upcoming change there. Middlesex may have a slightly better academic reputation, but it is close and motivated students would likely do well both places. LC’s financial strength/endowment is lower on a per student basis.
The two schools do share a lot of similarities, but I think overall size is likely going to be the determining factor here.