There is lots of cross-pollination between Mudders and other consortium students. Literally. One Mudder I know just married a CMC grad.
Mudd is known for having really good food, which draws students from other schools. There are plenty of Mudders who find time for extra curriculars, and those often include the other schools.
My only knowledge of CalTech is from 30 years ago. But then my impression was there wasn’t time or mental space for anything else but stem. I think of CalTech as wanting the specialist deep-divers in one Stem area. My impression of Mudd is that they seek out students who are explorers and connectors - people who are open to multiple fields of scientific study rather than prepping for one narrow major since birth. That is probably an over generalization for both schools, but you get the idea. It is not industry v graduate school so much that separates them, because deep divers and explorers can be found in both career paths.
The Mudd required course load is really intense and part of what makes Mudd Mudd. But the administration is really trying to figure out how to address the anxiety that permeates all college (and high school) campuses and maintain that rigor. Not sure about CalTech.