I think Charlie was more stringently blues-based; granted, he played the blues-scale in keys that were "wrong yet right" harmonically and thus sounds quite wacky at times but the point is that his melodicism was very blues-based.

Dizzy on the other hand was very blues-based too but I think he put in more "off"-notes and chromaticism and non-scale passing-tones in his solos so it was like expanded blues just like Charlie but a bit different in approach, like maybe Dizzy was more in tune with the expected tonality but put a lot of "off-notes" and chromaticism in there whereas Charlie was more "out" harmonically but more "in" melodically if that makes sense.

Then again, it could be because of the relatively more inprecise pitch of the trumpet compared with the sax that make me feel this way; the trumpet is of course a very "out" instrument in terms of pitch...