These instruments are not that comparable physically or acoustically. In the hands of master players, each can sound sublime.
I follow numerous jazz players on each instrument, past and present, including trumpet players such like Miles Davis, Louis Armstrong, Clifford Brown, Clark Terry, Blue Mitchell, Tom Harrell, Bix Beiderbecke, Ryan Kisor, Dave Douglas; and sax players like Stan Getz, John Coltrane, Coleman Hawkins, Charlie Parker, Lester Young, Ben Webster, Cannonball Adderly, Wayne Shorter, Joe Henderson, Chris Potter. I could go on for pages more...
I have learned one thing about trumpets courtesy of Latin jazz & ensemble genre music: the trumpet is perfectly adapted to play rhythmic lines/figures along w/the rhythm section in an ensemble, thus amplifying the overall rhythmic depth/impact. This capability has been fully exploited by many larger ensembles that play Cubano/Bop music over the years. To see what I mean, listen to the mambo cuts on Tito Puente's "Top Percussion," where sections of 2-4 trumpets double & build on the patterns played by various rhythm instruments.
Saxophones can do this, too--but due to the reed/tongue/embrochure interface (more complex physically than the mouthpiece/mouth interface of the trumpet), it's somewhat harder for saxes to exactly produce & follow very fast, repetitive rhythmic figures.