I was in the exact same place about two years ago. I had just finished up my BA in general music, and was torn between going to NEC for my Masters in guitar or getting a Post-Bachelors in Music Ed. to become a K-12 classroom teacher.
It comes down to how safe of a plan you want, and what sort of goals you have for your teaching career.
The Masters Degree is essential for college teaching, but that's a very competitive market nowadays. You can end up taking on a lot of debt and not make very much money. That said, if you're truly passionate about performing and teaching advanced, adult students it'll be the way to go. You can also look into a degree in musicology or theory for both job prospects and less performance pressure. If your goal is a career in college teaching, you'll probably have to look into some sort of doctorate afterwards.
The public teaching route is way safer. In most states you can get your preliminary teaching license in only one year. There are also far more full-time jobs with benefits, and with government jobs student loans are often forgiven after a certain amount of time. K-12 teachers still need to get a Masters (usually within 5 years of getting their first teaching job), but it's usually in education and mostly paid for. The teaching work, however, is entirely children and teenagers. Think general music, bands, chorus, etc.
In the end, I took the big risk and went to NEC. For me, it came down to two things:
1.) I truly love performing, and I'm willing to do the work to earn a place in that scene. Also, my end game is full-time college teaching, and I wanted a more direct route to that kind of work.
2.) Despite being far more financially secure, I couldn't see myself being happy as a K-12 teacher. Furthermore, I went to a school which specialized in teaching, and I could see just how much better my classmates were at it because it was their passion. I felt like I would be doing my future students a disservice if I went into that line of work. Also, many of my aforementioned classmates were brilliant performers when we were in school, and their playing atrophied as they taught classroom longer. I couldn't do that to myself.
If I was either more inclined to teach younger students, or less inclined to perform and teach college, I would have gone the K-12 route, simply because money-wise it made far more sense. I may still do it after I finish my Masters next year (instead of a PhD/DMA). I've met many accomplished full-time college faculty who got started as public school teachers. Also, from where I'm standing, I probably wouldn't get a DMA in guitar in the future, but rather a PhD in musicology or theory to be able to teach a wider variety of classes at the college level.
Sorry I can't be more concise about this; there's a lot to it!
In the end, I'd look long and hard at what kind of teaching you eventually want to do, and how much of a risk you're willing to take.
Check out SchoolSpring and Indeed and look at what sort of music teacher openings are available around you and in areas you'd consider living. See if there's something that you could see yourself doing.
2015 Alan Chapman Test Friederich CD/CO
2009 Cervantes Concert Milenia SP/PE