There may be a difference between the reeds of the Archaize sax and the reeds of the jazz.
Archaize sax tends to have a parabolic cambered reed, while jazz reeds have a straighter bevel. But it doesn't really matter, the sound is slightly different. Archaize sax requires the mouth to be tight, like a smile, maybe a little stiffer. Jazz is indeterminate.

Archaize sax may be like the clarinet we hear in orchestral music, generally avoiding excessive portamento and vibrato. Jazz is indeterminate, and there are often utterly obsessive glides.
Archaize sax doesn't seem to have much market, and there are no classical famous songs. It feels like a basic practice for saxophonists to learn skills. You can play a random section, the more dissonant the better, and then insist that it is jazz and improvisation.

Archaize sax emphasizes technique (timbre, breath, various techniques, etc.), interpretation of the work, and finally the pursuit of the most pleasing or harshest presentation within the scope of the work's requirements. This statement is reasonable whether it is for harmonic instruments or melodic instruments or even orchestra performance. Jazz emphasizes theory, because the theme and harmony of jazz music are determined, and the pursuit is to play tricks (improvisation) under the same harmony. The audibility of this trick is actually not as good as that of classical music. The reason why everyone feels so emotional is that the basic harmonies behind this riff and the drums behind it are very jazzy.

Through the above introduction and analysis of Archaize sax, hope it helps you.