I love and advocate the books Art of Saxophone Playing, Teal Saxophonist's Workbook, and Liebmans Developing a Personal Saxophone Sound. I think the presentation of concepts from both schools of teaching resonates with me at different times in different ways.
Funny, when I started studying privately in college, it was "Teal method." The last few years, I had a very fine teacher and saxophonist (Dr. Daniel Goble) who used primarily Joe Allard concepts. Everything I learned from studying with Dr. Goble totally resonated with me and really helped me. I'd also add my first two private teachers didn't discuss jazz players much at all and saxophone wasn't the primary instrument for either (oboe, clarinet).
Goble immediately connected with me when he started talking about Michael Brecker, Joe Henderson, Cannonball Adderley with the same respect as Mule, Londeix, Allard, Sinta, and Pittel. He impressed upon me the importance of flexibility to get the sound you hear on whatever mouthpiece you were using, without working so hard. All those overtone exercises and matching the "overtone feel" to the standard fingerings along with tongue position, those concepts generally identified with Joe Allard helped me tremendously. I think we did lower my pitch center and put a little more lip out (cushion) to allow the reed to more freely vibrate as well. There was also a lot of focus on listening and hearing the sound.
I guess since that time (late 1980s) I do use more of the Allard based concepts as far as tone production, but I still reference Teal's methods too. The vibrato studies, interval exercises, and long tone exercises in Teal's Saxophonist's Workbook are great, although I guess those are pretty universal. With all the great stuff in the Teal books, the lack of discussion on tongue position does seem to be an omission for me as that also helps a lot with articulation. I always imagined if you studied with Sinta or Teal there was a lot of work "outside the book"...