Is research experience or hospital volunteer work more important for medical school?

Everyone volunteers. Everyone cleans up the beach. Everyone volunteers for meal on wheels. Everyone volunteers to do patient transports. Everyone tutors high school kids.

That was I was told by someone who works at the admission department.

Hint: It no longer stands out.

I'm not fully sure if one is better over the other since I'm not a medical student, but from my experience as an engineering student, a research experience has a lot more benefits in general and are pretty important for Grad/Medical School. When you work as a research intern you more than likely get paid (and in some high-end research places they can pay quite a lot) Also, if you've already done some volunteering at a hospital, then that should look good already on your application to medical school.

The only thing about research experience is that you have to apply for it and they can be pretty competitive since they are pretty much like applying for jobs. If it was me, I would apply to a couple research positions for undergrads and see if you can get one. If not, then you can just do volunteer work at a hospital.

Wow, I agree about trying to fit in too many activities being too stressful!

You would probably better off getting research experience. While hospitals depend on volunteers for a lot of things, not all of them are related to the kind of work that a physician would need to do.

Good luck!