I became an EMT while getting my first degree many moons ago. After I got out I actually went to paramedic school at night and worked part-time as a paramedic for about eight months mostly a Saturday or Sunday every week. I moved with my primary career and never picked it back up. Yeah, it helped. I learned a lot more in that program than nursing school, and I did maintain NREMT-P status for a lot of years. Fortunately, knowing the right people got me a physician's oversight signature on my credentialing papers even without being employed anywhere. I gave it up finally in 08 I think but managed to hold onto my state EMT-B cert.
You're going to find some differences. One, nursing school is barely going to touch on, if at all, anything you do as an EMT. Two, nursing school teaches by the funnel method. They pour it all in and hope it comes through the other side without going over the side and oozing away which results in a less than great learning environment. EMT and paramedic school taught stuff to teach it, and we did far more clinicals and got way more hands on practice than in nursing school. In nursing school you'll eventually be assigned one individual patient or two and do their nurse work. If you're chained to a non-acute patient, as many of them will be, you don't really get do anything exciting. I still stand by my nursing school clinicals as being devoid of any learning experience. In medic school, etc. we floated around seeing and doing whatever we wanted so we could get maximum exposure and practice. I had classmates who never stuck a single IV, for example, because on their day their patient never needed it. Yeah, it's learned easy enough, but a RN shouldn't enter the workforce without having gotten that down, IMO.
You'll take a more independent and action-directed approach where as most of my classmates and instructors wanted to talk about something or do things in groups rather than going in and getting it done and moving on. Also, at least after paramedic school (can't say that EMT helped with this) my assessment skills were higher even after all that time. Because of the way I was taught back then I learned it and when it came time to do it again I picked it right back up. After a couple of IV pokes I was back in the old swing of things with no problem. You'll also have already learned some of the things nursing school will teach so you'll have a foundation.
Nursing teaches a lot about longterm general medical problems, and these aren't so much in the dedicated curricula of an EMS program. You may learn about things you never thought about or believed to be an issue that nurses thrive on. Nursing, for example, is really concerned with people's bowel movements where as in EMS we couldn't give a rat's tail if they could poop or not. The same goes for skin assessments as an example.
You'll learn that nursing supposedly monitors the human condition and addresses the response to given disease, treatment, etc. I can't even remember nursing's definition offhand. Nursing, as a professional body via NLN and others, tries to distance itself from anything of a medical-ese nature and align itself more with such areas as sociology. Nurses do "nursing assessments," have "nursing interventions" and write care plans, which coming from EMS, you're going to think are completely bizarre. If a duck is a duck, call it a duck. No, for nursing it'd be "fowl of flight related to an aquatic environment as evidenced by pedal design, feather overlap, and feeding behavior." If duck were a known medical phrase nursing school is going to teach you not to say duck or *gasp* risk practicing medicine.