how do you use octatonic scales in jazz composition?

Question

Which one do you use? the one starting with a whole tone or half tone?

Answer 1

Use them with diminished chords. If you've got a half-diminished 7th (or min7, b5) use the one that starts with the half-tone. If you've got a fully diminished 7th, use the one that starts with the whole-tone. Then you've got the 7th in the scale along with the other notes in the chord.

Answer 2

octatonic scales are useful for writing a melody line over a diminished chord. If you start the scale on any note of the chord, it will include the notes of the diminished chord -- it doesn't matter if you start with a whole step or half step. Just use whichever one sounds right.