The biggest change I underwent so far was when I started playing my Selmer Series III and a c* mouthpiece. At that time my embouchure was pretty tight. I imagined a slender sound with a lot of projection. My phrases were also very sustained with a lot of compressed air. Then I changed. I wanted to be more flexible. Ease of playing became more important than sound. I got an AL3 mouthpiece by Vandoren. But it didn't work on my Series III. The tuning was terribly off. So I looked for a horn that was compatible with the AL3. It was a Reference by Selmer. For years this was already a very popular set-up in Holland with conservatory students. And I understand why. It's easy to play. The AL3 seems to be a sort of almost Buescher like mouthpiece with a small tip and short facing. The legato is very easy and sound production hardly requires air. It's a dream. But of course, every mouthpiece and set-up has its disadvantages. This one as well. It needs more input, more personality from the player. It's very easy to produce a sound that is average and to play with a little air support. It needs more conscious artistic investment. Yes, apparently a mouthpiece can play too easy!
So I had to change embouchure with this set-up. More relaxed. Less compressed air. Supported, but with less effort. I had more energy left to focuss on the music.
The last step (for now) in this personal development was to have the under lip more outward. Somehow it changes the relation I have with the reed. It becomes less important. Still essential, of course! But I can still have an ok sound on reeds that are less good. I am not sure what happens with more under-lip outward. But it seems to give more control. And the reed needs less air to vibrate.
My view of embouchure as I explain it my students at the Fontys conservatory:
The upper teeth go on the mouthpiece. The under-lip goes over the teeth and the lip goes on the reed. Then you push the muscles around the mouth forward, like saying 'ooh'. That's it. Everything else you do is too much. The rest is relaxing. Well, more or less.
Also the position of the tongue is very important. It should not be flat in the mouth but the back should go up almost in between the molars. The tip of the tongue stays as close to the reed as possible. This is the basic position of the tongue.
The intonation is done with the tongue, not the lips. This is a much heard misunderstanding. The lips hardly have influence on the intonation.
And as I have found out, the amount of under lip that is out or in is of great importance.
For classical saxophone, many sax teachers will tell you that your chin needs to be flat. Although I agree, I don't think it's good have this as a basis for practicing. Firs of all, it is non musical. The basis of practicing needs to be sound conception. Not mechanics. In the end I find that most students (if not all) play with a flat chin.