I've been doing a lot more research, and it does all depend on where you want to teach English. If you want to teach in Germany, Eastern Europe, or the Far East, a Master's degree in linguistics with at least some TEFL certification really seems to be put you at the top of the top (a Master's degree in any subject with TEFL certification seems to put you up close to the top, too). However, if you want to teach in the USA, you almost need a BA in TEFL to make a good living...or so it seems. But I don't want to teach here.
By the way, in the UK, Canada, and Australia, my degree won't do much there, either. Each one fo these countries has specific criteria.