Hello! I am not an RN, but I am currently an EMT-B student and working on pre-reqs for a BSN program. I think Vent really hit the nail on the head. EMT courses focus on skills, but nursing programs (especially BSN) are much more academic. You may be able to take a BP with ease while the other students struggle with the cuff, but can you write an APA paper in perfect format? Are you good at statistics?
The way I see it, the advantage of being an EMT-B prior to getting into nursing is having a slight headstart on things like building patient rapport and taking vitals, and also that you're more likely to know that you're in the right field. If you work as an EMT, you'll already have experienced some of the ins-and-outs of working in health care, like the politics, paperwork, a-hole patients, a-hole coworkers, crazy families, vomit, poop, etc etc.
Just as many people have misconceptions as to what EMS is all about, many nursing students have misconceptions about the career. Some of the misconceptions are common among the two professions. If you've already had some of these misconceptions shattered by working as an EMT, then you don't have to go through that process when starting off as nurse and you're more likely to get into nursing for the right reasons.
Anyways, good luck!