One of my sons visited and applied to all three – MIT EA, Caltech EA and Mudd RD. Mudders have a large math requirement, Caltech has a similarly significant physics requirement.
S1 was a math/CS guy – didn’t like the vibe at Caltech; he sat in on a liberal arts class and didn’t like it at all. Felt the students and prof were disengaged. The folks he knew who went there were very intense and S likes balance between classes and nerdish fun. When we visited Mudd, the profs came out of their offices (in the dead of August) to talk to him. Mudd seems into integrate STEM and humanities better. He really liked Mudd – the classes, the students, the profs. He would have spent two years doing independent study math because he had already completed half of the UG math sequence, and that was not the way he wanted to go. My sense is that engineering is a bit more generalized than at Caltech, but my info may be outdated. MIT would have required lots of engineering courses in the CS major, and he was more of a theoretical CS guy. He also wanted to avoid bio and chem core like the plague. He found his peeps on East Campus in late April, but by then he had pretty much decided.
When he got his decisions, he made a matrix of qualities and factors that were important to him, weighted them by importance and ranked them by strength. Was hard to dispute his decision making process.
He wound up at UChicago! Top math, great theoretical CS, great humanities (even if it kicked his tail). They were generous with placement, he took a bunch of grad courses, and his feeling was that if he was ever going to study humanities, UG was the time and Chicago the place. He had some regrets about not going to MIT and some about going to Chicago, but he spent two summers at MIT and that seemed to strike a balance.