I'll wade in with some comments about Arthur Murray Studios. I've been taking lessons for about three years, all at various AM studios. My experience has been very positive, but I've also been very lucky with regard to the specific studios I've been at, and also with regard to my instructors. The instruction at any studio, AM or independent, is only as good as the teachers who are there. Even with the AM "method," and a common syllabus, not every AM studio is a cookie-cutter version of another.
A key thing is to COMMUNICATE with the instructor, and the franchisee. If you want to focus on technique, ask them about the best way to focus on that - preparing for competitions is a good incentive for both you and your instructor to focus on those details. If your instructor knows that you really want the details of technique, they may plan your lessons slightly differently than they would if they thought you wanted only a "social" dance education.
I, too, wanted to focus on style and technique in dancing. I've never really been all that caught up in "method" of teaching - dancing incorporates a entire range of elements from poise and posture, to footwork, to lead/follow, etc. Just because one "method" focuses on, say, footwork first, whereas someone else's "method" focuses on, say, posture first, doesn't mean that one method is right or wrong, or better or worse - in the end every "method" aims at working on all the elements. A lot depends on how long the student can stick around to learn each element and how to put them together. Each element may need to be learned in various "layers" - so that, for instance, you are not going to learn all the hundreds (or so it seems!) of intricacies of Cuban Motion in one lesson - you will probably start with a very basic component of Cuban Motion, and as you become more comfortable with it, the AM "method" will refine it, add another component to it, etc. Some people who slam the AM method may have stopped taking lessons before they learned all the components of each element, and feel as though they didn't learn anything when they find out that other people focus on different aspects of an element. I'm at the point where I can take a few coaching lessons from independent coaches, and they have told me that I've been taught some pretty solid skills.
AM does try to "sell lessons" and they are criticized for seeming to push people into long-term contracts - keep your eyes open, and know where you want to set your limits. But also be aware that if a studio knows that they have, say, 15 lessons to teach you something, they can better plan your lessons, than if they don't know from one week to the next whether you'll be back or not and then try to cram too much into a lesson.
AM wants to sell lessons, but if they turned out consistently awful dancers, no one would take lessons from them. My instructors have been just as committed to teaching people to dance well, and I have seen some pretty darn good dancers who learned through the AM "method." Be realistic and be tolerant with regard to reaching your goals, and have some fun along the way!
I've probably gone on too long, so feel free to e-mail me privately, if you want to delve into any specifics. Meanwhile, I'll get back to preparing for my next competition. . . .