I wouldn't say EMTs a dime a dozen... people who volunteer in hospitals are a dime a dozen or volunteer with the underserved maybe. Don't get me wrong, many people get the EMT cert, but much few actually use it which is the most important part. Having the cert won't give you any props but the experience you gain from it (actually working in healthcare, taking care of patients etc.) might give you some insight into different sides of healthcare that you haven't had previously. At least that's been true for me..
It was hard to balance working night shifts and school for me, so scheduling is something you'll have to consider when looking into ambulance companies.
Also, just so you know, as an EMT you'll mainly be interacting with section 12 patients, patients with schizophrenia, dementia etc who often are very agitated and don't want to be wherever they are not patients with learning disabilities if that's what you were looking for.
Ultimately, I wouldnt say that either option is anything that would make an adcom lose their minds for you rather it's what will give you the best experience to write about/talk about in your apps