I don't think anyone's ever quite figured out what is responsible for a players "sound" and I wouldn't want to put it in the form of percentages, but here's a few points worth considering -
Firstly...
the sound you hear as a sax player is different to what an audience member hears. This is due to a number of factors -
Proximity - you're a lot closer to the instrument than anyone else, so you'll hear a lot more of the details of the saxophone's sound
Physical contact - not only can you feel the vibrations in the instrument, you've also got the reed vibrating in your mouth and the air column vibrating in your oral cavity as well as the mouthpiece resting against your teeth. P
lus there's the effects of bone conduction - "Bone conduction is the conduction of sound to the inner ear through the bones of the skull. Bone conduction is one reason why a person's voice sounds different to him/her when it is recorded and played back. Because the skull conducts lower frequencies better than air, people perceive their own voices to be lower and fuller than others do"
http://en.wikipedia.org/wiki/Bone_conduction
So as players we hear things that other listeners just won't notice and the differences between different horns, mouthpieces, reeds etc are more apparent to us and also our perception of our tone is unique to us
I've made recordings of myself with different combinations of mouthpieces and different makes of saxes and apart from things being a bit brighter or darker, I sound pretty much the same.
So what is it that gives us our sound?
Well, that's like asking what is it that gives us our individual speaking voices -
"The sound of each individual's voice is entirely unique not only because of the actual shape and size of an individual's vocal cords but also due to the size and shape of the rest of that person's body, especially the vocal tract, and the manner in which the speech sounds are habitually formed and articulated. (It is this latter aspect of the sound of the voice that can be mimicked by skilled performers.) Humans have vocal folds that can loosen, tighten, or change their thickness, and over which breath can be transferred at varying pressures. The shape of chest and neck, the position of the tongue, and the tightness of otherwise unrelated muscles can be altered. Any one of these actions results in a change in pitch, volume, timbre, or tone of the sound produced. Sound also resonates within different parts of the body, and an individual's size and bone structure can affect somewhat the sound produced by an individual..... There are seven areas that may be listed as possible vocal resonators. In sequence from the lowest within the body to the highest, these areas are the chest, the tracheal tree, the larynx itself, the pharynx, the oral cavity, the nasal cavity, and the sinuses"
http://en.wikipedia.org/wiki/Human_voice
Given all these variables, it's no surprise that we all sound a bit different or that skilled players can shape the sound of the saxophone so much. It also explains why you'll never sound exactly like John Coltrane....
Mouthpieces -
There's no doubt that many mouthpieces will have an effect on your sound, particularly if you go to extremes. A high baffle mouthpiece like a Dukoff D, Lawton BB, Lebayle Studio, Guardala King etc will always sound bright and edgey and you'll never sound like Johnny Hodges with something like that, and at the other end of the spectrum a vintage large chamber mouthpiece of the kind that was made in the 1930's will never give you a David Sanborn type sound.. well, I say never, there's bound to be someone who can do it, but you get my point.
Choice of mouthpiece is a personal thing and involves factors like how it feels in your mouth, how it responds, the amount or lack of resistance ("freeblowing"), did your favourite sax player use one and can you afford it, as well as the obvious tonal qualities...
I tend to think that the response of a mouthpiece is one of the main factors in what I use - I like one that responds quickly with little effort and works well in the altissimo register and helps me play multiphonics, hence my choice of a Lawton BB. Other people like a lot of resistance to push against and like to "put a lot of air through their horn" - generally these are the vintage Otto Link enthusiasts. I've found that to get the best out of a Link you have to work at it and really learn to use your embouchure, oral cavity, throat etc, so you spend hours practising long tones when you could be having fun. The payoff is you'll get a big fat sound (and angry neighbours), whereas the highly responsive, high baffle mouthpieces will tend to sound shriller and brighter.
Mouthpiece makers like Theo Wanne have tried to combine the two, so you get a fast, easy to play mouthpiece with a full rich sound. I suspect the PPT and Morgan Fry's Rhodium Large chamber also give you the best of both worlds..
Skilled mouthpiece technicians can do all kinds of things to enhance the playability of your mouthpiece and an accurate facing curve usually helps a lot.
Factors that will affect the sound of a mouthpiece include the height and shape of the baffle and the size and shape of the chamber. The length of the facing and thickness of the sidewalls can also have an effect. The material the mouthpiece is made of may also be a factor, but given that the thing is in contact with your teeth and you're hearing some effect through bone conduction, it's difficult to determine how much effect the mouthpiece material has on the sound heard by the audience. There's been scientific research, but nothing conclusive. There are too many variables involved.
Another thing to consider is that you'll tend to adapt your playing to how you perceive the mouthpiece to sound. - stick a Dukoff D8 on your sax and you'll soon end up in Sanborn territory and there won't be many Ben Webster licks coming out of your horn.
Listening the the sound samples on Steven Neff's excellent website, you hear him playing differently according to how he hears each mouthpiece he reviews
http://www.neffmusic.com/blog/category/mouthpiece-reviews/
and there's no doubt that there's a relationship between what we hear and how we play
Saxophones -
There's been a lot of discussion on various forums about body tubes, tone holes and all the rest of it. I'm not going to open that can of worms...
Over the last 50 years the R&D departments of companies like Selmer, Yamaha and Yanagisawa have improved the intonation and evened out the response of modern saxophones. This has, in the ears of many vintage sax enthusiasts, also evened out the tonal differences between the different saxophone makes.
Sure you can, as a player, tell the difference between a Yamaha and a Yanagisawa, but could you tell the difference if someone else was playing them? I can't.
While I wouldn't deny for a second that having a modern sax that plays in tune and is little effort to play is a very wonderful thing, there's something about the experience of playing my old Martin that just can't be had on a modern horn. Mostly it's bad intonation and rattling noises.... or is that old age catching up with me...?
The attraction of vintage saxes (and mouthpieces) is at least partly due to the mystique and mythology - your hero played one, so you must have one just like his etc - plus the sheer loveliness of them and the antique collector mentality. A lot of it's psychological, if you've got a Mark 6, you'll feel better and more confident and play better. Or at least try harder in an attempt to justify your expensive investment.
Conversely, a lot of pro players are leaving their valuable Mark 6's at home and gigging with modern instruments that you can actually get spare parts for.
I've heard music college students get a nice warm sound out of a Yamaha 4C and a YAS 275, so fancy equipment isn't a necessity. Practice will bring results.
A well set up, leak free horn with a nice fast action that plays in tune is all you really need..
GAS -
I think a lot of the neurosis for buying mouthpieces etc is driven by wanting to sound different than you do already. We've all got our own individual sound, we're just not happy about it and would rather sound like Dexter Gordon. But even if you could travel back in time and walk into a Blue Note recording session and borrow the great man's sax, the results still wouldn't sound like him..
Years ago when I was a teenage guitarist I used to read in guitar magazines that you could only get your own sound through years of patient effort, but when I listened back to recordings of my own primitive efforts, I could tell immediately it was me. So I realised that I already had my own sound, I just didn't like it very much.
My answer was to accept this fact and learn to like, or at least tolerate, my own sound instead of chasing the mirage of some mythical sound that I could never achieve. I stopped worrying about my tone and got on with enjoying my instrument.
I'll always sound like me and you'll always sound like you - be happy...
obviously all this rambling hasn't answered your question, but it gave me something to think about while I was waiting for the bus...