Hi,
You may have already found your answer as it is now October, but, just in case you haven't. I am currently pursuing a terminal MA but am planning on going into secondary education after I finish. When I made the decision to enter an MA program I wasn't sure whether or not I was going to go on to the PhD or secondary ed, but I've sense resolved that decision.
So here's some pros and cons:
M.A.T.
Pros:
Certification! (but this isn't an issue for you)
More Teaching Experience (though if you can get a Teaching Assistantship in your MA, you may be in charge of some of your own classes, however, obviously high school teaching isn't the same as teaching college students)
Shorter (at least in my state, you can get done with MAT degrees within a year if you take summer classes)
Will likely better prepare you for classroom management, lesson planning, and effective teaching strategies (and dealing with state curriculum requirements, etc. - although again, this might not be as much of an issue in private schools) - I'm not one of those people who is of the opinion that education classes are pointless, I think extensive pedagogical training is essential to being a good teacher(not that I have a lot of experience though)
You will likely need a MAT (or some form of Masters in Education) if you want to get into administration
Cons:
Depending on the program, I would say there are usually less funding opportunities.
Substantially less engagement with your subject material (however, this could be an advantage, there might be more jobs in world history or civics than American History)
Maybe more rushed.
I think Private Schools actually really value & are willing to hire people with advanced degrees in their subject areas.
M.A.
Pros:
Often funded
Teaching Experience (if you are funded through a teaching assistantship)
Really intense engagement with your subject material that you would probably not have if you don't pursue the degree. Also, the classes are waaay more engaging then they ever were in undergrad (the students & the teachers are much more into them)
Again, I've heard that Private Schools look at MAs as huge advantages when hiring, but I'm not positive.
Cons:
No certification (again, not a problem for you)
Doesn't prepare you as well for the challenges of the high school classroom (but you have experience, so perhaps this isn't a problem, if you are worried though, volunteer with high schoolers, or harder to teach groups when you are in your MA)
It is hard to be as competitive (or sometimes as motivated) as the other students in your cohort when you are not planning on staying in academia, and you can feel a little out of place. That being said, at my school, students (& professors) understand that academia isn't for everyone (not even every grad student) and are very encouraging of those of us who might want jobs outside of academia.
Even though it's not a PhD, it is still very hard work.
You can always get them both....especially because I think sometimes schools will assist with the costs of masters degrees in education (this may be only in public schools though)