Having worked with many different musicians over the course of my career, I have often gotten into discussions regarding playing jazz and classical music. Some feel you should focus only on one of the two genres because it is impossible to do both well (I disagree with this) others try to learn as many styles as possible because you will never know what kind of gig you will be called for (I fall into this group). I feel we should be open minded, flexible musicians. Playing jazz and classical saxophone requires players to think differently and playing both styles can take us out of comfort zones and make us better players as a result.
So, how does one become proficient in jazz and classical music? What is the best way to go about this? Well, there is not one specific way to go about this, but here are some approaches that have worked for me as a saxophonist.
First, listen to the right music and players. If you are working on classical repertoire listen to classical players (not just saxophonists, listen to other instruments as they can provide great insight on interpretation) play the works you are studying. Listent to several players play the same work to hear their interpretation of the work. The same applies to jazz playing. listen to the prominent players. Like a teacher once told me: "If you are working on classical music, don't spend all of your time listening to country and western music."
Second, have the correct equipment. If you are playing jazz have a jazz mouthpiece and reed setup and the same goes for classical playing. Furthermore, you need to learn the correct embouchure for each type of playing; the jazz embouchure is very different from that required for classical. Don't try to play the Bozza Aria with a Dukoff, it really won't work well at all.
Third, you really have to learn to be convincing. You have to get in the right mindset for a given type of music. When you are playing jazz you want the audience to think that you never play classical and viseversa. For some players the change in equipment is enough. But, you may have to go as far as playing jazz on one horn and classical on another. For years I only played jazz on tenor and classical on alto. That helped me get in the correct mind set for the differeing styles (If you are going to do this, I wuold recommend using the alto for classical because most of the literature is for alto saxophone).
Fourth, and most obvious, you have to practice both styles. It is best to spend a few hours on jazz and a few hours on classical each day if possible (I did this while working on my masters up to three hours a day on each). But, I know that life often makes this impossible, so you may have to develop a weekly practice routine. As is often said "there is more than one way to skin a cat" so you can develop a routine that works for you. Just make sure it is consistent. I have had succes working in streaks going weeks, months, or sometimes years focusing on one style (I did this with classical playing while working on my doctorate), but I would only recommend this approach for more experienced players who already have a solid foundation in both styles of playing.
There are many ways to approach playing both sides of the horn. For those of us who play jazz and classical saxophone, please include your approaches. I would love to hear how you go about things.