Well, this is just my opinion. I am currently completing the process of becoming a CAPPA CLE via the distance program- I believe all in all, books, etc. included, it should cost me about $400 dollars, plus the $50/year CAPPA membership and $75 re-cert fee required to remain certified.
I investigated a number of options (for both lactation educators AND childbirth educators, though in the end I decided to go for the CLE because I work with PP mothers and their babies; don't get any time in L&D).
Of course, LaLeche League is the only place you can become a LLL teacher.

I'm not telling you anything you don't already know there. CAPPA has a very reasonable-fee CLE program, though, so if you haven't checked that out, you should.
Bradley and Birthworks are both registered trademark classes; in other words, to become certified through either of them would mean you are certified to teach THEIR class and follow the structure that *they* provide you. You are basically a representative of their company, teaching classes based on their respective philosophies. CAPPA, on the other hand, is much more liberal in that respect- they do not teach you a specific philosophy, but rather have you do a lot of research on your own and then back you with their certification, enabling you to go out and structure your OWN classes or lectures, working with more than one philosophy to create the best class you possibly can.
To me, this is a much better idea. Very few people subscribe to only one school of thought, and the best teacher is one who can reach to numerous sources of information and then combine them in a way that provides the most comprehensive and applicable education for his/her students.
Not to mention, CAPPA is MUCH more affordable, and they have a distance program that allows you to do much of the work on your own (ie, not necessarily having to go out of state to a $600 conference just to prove you're serious about the certification!).
All of this just depends on what YOU want to get out of your education: Are you comfortable sticking to one main philosophy, or are you looking to provide a more rounded class? Neither is correct; it just depends on what you're looking to do with it.
I hope that helps a bit! Let us know if you have any more questions; I've spent quite a bit of time investigating this.
The thing I like in particular about the CAPPA CBE course is that they embrace natural birth, but accept that it's not for everyone and so include legitimate options as far as epi's go, etc. I'm a pretty moderate person, philosophy-wise, and this was something I personally believed in.