The simple answer is, "I don't know."Pete: I am no expert, but I've owned a few horns in my time and played a lot more than that. I'm wondering if the normal variances among similar saxophone models has been factored into your comments. In my experience, I've found that numerous instruments of the same model have different tone, with a few exceptions.
I would think that it would take the playing of MANY of the same model to draw any conclusions as to overall tone. Wouldn't a mass of Conn-o-Saxes or F-Mezzos produce a variety of tones depending on numerous extraneous factors? What if you had many HP horns and LP horns (like Dr. Cohen's two sopranos); maybe the next comparison would produce a better LP than HP tone?
I have two Buescher TrueTone LP sopranos, silver-plate, about 4500 numbers apart (237xxx and 233xxx). They are different from each other, albeit both are good players.
I once tested numerous Yamaha pro-line altos and found a world of difference among them.
The only saxophone model that I've found with a consistent tone was the Selmer Ref 54 altos. While some played better than others, they all sounded similar.
As to clarinets, I have a C-clarinet and while it plays most of the same notes as my Bb soprano clarinets, the C has a definite "smallness" in sound while the Bb models all seem to have more depth in their tone when playing the same notes as the C.
I do agree with you that, when you're talking vintage instruments, there can be significant variances between them, even if they are only a few serial numbers apart. However, you then get into the arguments of how much the player can compensate for the tone and how do certain makes/models get a reputation for something (like, "Yamahas are bright horns").
In the case of a Conn-O-Sax vs. an Eb alto, I think it's both the design and how it's played. It was demonstrated, on another thread, that the Conn-O-Sax (and F Mezzo Soprano) have a bore much more like a Bb soprano and have a mouthpiece that matches. The Eb alto should be darker and fuller for this reason. You could also argue that it's the way the horn's played: you can play the C melody tenor so that it has more of a reedy, bassoonish quality or you can say, "It's just another tenor" and play it as such.
With the two Evette-Schaeffer sopranos, for HP vs. LP? I dunno. All I can say is that I could tell a difference and I liked the HP one better. (FWIW, I seem to remember something saying that HP was "better" in some way, but the reason why LP won out was because you didn't have to tighten your strings as much, thus saving wear and tear on your $10 million Stradivarius.)
In your experience with the C clarinet, just to support SOTSDOs point (so good he posted it twice), I'd wonder if it's the instrument, not the pitch. Or the mouthpiece. Again, too many variables. I've played all of one C clarinet (which, oddly, was HP), one A and two Eb sopraninos -- ever.
Finally, you've got the question of player vs. audience: the player might say that horn X is too stuffy, while the audience can't hear any difference. I can accept that.