Mudd is much smaller, more holistic and less focused on specific engineering or CS detailed knowledge. They really are quite different environments and curriculums. There are a tremendously larger number of graduate classes to take at CMU, as they offer PhD programs in CS. CMU is more compartmentalized and CS has a less good relationship with say EE or other engineering departmentsat CMU. Mudd is one happy school. You really should visit to determine which fits you better. CMU has more research projects with lots of undergrads participating, on campus. Mudd, you really need to go elsewhere, in the summers, its more of a teaching focused school.
CMU has nice theatre and music to distract you from the overwhelming workload. Mudd may be more happy go lucky, more upbeat, better weather. Mudd has truly difficult grading system with perfectly brilliant students earning Bs regularly.
CMU is a broad schools with more majors to pick from, should you somehow change your mind, but some restrictions on transferring around to other colleges and a quota on ECE majors in Engineering. .
Mudd has a very small number of majors, and they allow you to pick your major
and do not try to force you to select it in high school, as CMU attempt to do.
Mudd, for instance does not offer economics, so all that great business related math is not really well covered at Mudd should that interest you. (Claremont McKenna offers econ, as does Pomona, but you cannot be an economics/math major at Mudd, you would have to transfer, if you decided stats/econometrics interested you.
Mudd and CMU can both lead to PhD programs in CS, but with Mudd, if you do not have As, it can be a problem to get in. U of Cal, most of the campuses, the grad programs recognize Mudd as hard and take students with lower GPAs, but Illinois and UW Seattle may not! CMU may be slightly easier to earn those As, from what we hear, but all depends on your math skills
and what courses you take.
I have heard of faculty at UC San Diego arguing to let in good Mudd grads in chemistry with lower GPAs.
Ask about this GPA issue at Mudd. Its just ridiculously hard to get As there.
For hockey, go to RPI !!