While Coleman Hawkins and Sidney Bechet differ in so many ways, one trait these saxophonists share is their masterful skill at playing a melody. They don't just state the melody though, they declare it. This rhapsodic approach is highly emotive and rhythmically flexible, perhaps showing some of the strengths inherent in the saxophone at its best.
Here's Hawkins' operatic rendition of 'How Deep is the Ocean' from 1943:
And the spine-tingling 'Bechet Creole Blues' from Sidney with Claude Luter's band in 1949: