The biggest issues we face as jazz performers are the difficulty level of the key as it lies on your instrument and whether or not there is a negative quality to the sound from playing it in a higher or lower register. To vocalists this is called tessitura. The goal in choosing a key is to avoid drawing attention to it. I've heard some singers take "low is sexy" too far, the result being a distraction from the actual music. There are some singers who challenge themselves to try melodies in whatever key the band chooses, such as the wonderful Nancy King. As musically impressive as this is, most people can settle on a range of a semi-tone or two where the sound of the song is comfortable for them. I vaguely recall playing a song for a singer in C who found the piece high. After attempting the lower key of B, I was asked "Is there a key in-between those two?"
The actual audible difference between two keys that are adjacent, like B and C, are more in the performance than in the sound- on many instruments certain keys are more natural, such as C on the piano or via transposing, Bb on the trumpet. One of the first solos I transcribed was Chet Baker on “Tune Up”. The first two lines of the trumpet solo are melodic and simple, building to a flurry of excitement in the third line, and releasing in a simple fourth line. This happened again in the next chorus. On the piano, the faster line was quite challenging to me at the time, I worked out fingering and ran it several times. Only later when I tried to play it on the trumpet did I realize the faster line was in the ‘easier’ key of C (concert Bb). While Chet Baker isn’t by any means limited by key as his later playing in the same solo shows, there still is at some level a comfort level associated with an easier key.