My own view is that in a full-size, busily-working jazz band, the clarinet's job is more important than the trumpet's. I have written on this topic before. As I implied then, a really good clarinet-player can turn an ordinary band into a great band.
It's true that trumpet playing can be very tiring on the muscles around the mouth. And it's also true that the trumpet player needs to have plenty of tunes accurately stored in his memory (though this is easier than some may believe).
But a good clarinet player has to know the chord changes of every tune - either by rote or intuitively - and he has to be a master of rapid arpeggios. His fingering must be confident and fast. He must also be skilful at throwing occasional long bluesy notes into his playing - usually flattened thirds and sevenths.
But what about the rôle of the trombone in all this? I consider his job extremely difficult too. He needs to know the harmonic progression of every tune the band plays (either as a result of hard graft in learning the chord sequences or by developing an amazing ear for the bass-line of the successive chords). He has to push the band along through the chord changes. This frequently involves (starting on the fourth note of a bar and moving on to the first of the next) taking the harmony from the root of one chord to the root of the next by means of a glissando or direct punching out of the notes.
But he must also have a huge repertoire of tricks and phrases. He should be able to take on the melody for an occasional chorus - to give variety to the presentation. And he should be a skilful user of mutes: a good range of trombone effects is possible to embellish the music.
So I come to no conclusion. To play any of these instruments really well in a traditional jazz band is very hard work and requires a great deal of practice and experience.
After reading the above, Barrie Marshall - a well-known reed player in the north of England - sent me these observations:
Another reader in his own blog (http://www.wilktone.com/?p=4545 - well worth reading; let me recommend it) has made the point that clarinet and trombone players SHOULD always learn to play the melody line accurately. The reasons he gives are:
(1) this will help the player to avoid clashing with the melody notes; and
(2) there may be occasions when a clarinet or trombone needs to play the melody, either as a pleasant variation on usual practice or because the trumpet-player could be absent ill.
These are very good points.