First off it depends on what your experience as an EMT or medic was. If you worked as a volunteer and saw a total of 30 patients in your career, probably not much impact on your future. If you worked full time for a few years and saw 2500 patients, that is a lot of clinical experience. It's difference from being a resident but it helps in that differentiation of "sick" versus "not sick." I think it gives you a bit of a leg up in the beginning of med school, you feel comfortable talking to patients, doing an exam of some sort. But your medical school experience sorta washes out any previous experience. You see so many more patients in medical school that what kind of medical student you were has a much bigger impact on what kind of resident you will be than what you did before med school.
As to field, the issue is that there aren't many chances as a pre-med to get to do surgery, or cardiology. So while EMS is similar to EM, most EMTs go to med school an branch out ito other fields (though some like me certainly stay in emergency medicine.) Most people who like EMS tend to like fields with acuity and some hands on activity. So a lot of EMTs and medics tend to be drawn to things like critical care, anesthesia, cardiology etc.