Both my kids visited CMU as well, and neither one applied. CMU seems to be good place to be from, as opposed to be a good place to be. Nobody we saw on the tour, either time, looked happy to be there. I actually wrote about this a couple of years back:
In contrast, the Rice visit was a joy for both my kids. It’s easy to see why they routinely get the “Happiest students award”.
Among these three schools, there are very marginal differences in terms of quality of engineering education. Find the place where your child will be happiest.