IMHO the two fields are very similar. I, and many other airline pilots with whom I fly, are musicians (to some degree at least). For me, the music is simply a pleasurable hobby these days, but for others, it's much more.
You could truthfully say that both professions are "performance" professions (i.e. there is a certain required talent or skill-level; these skills must be carried out real-time, watched/evaluated/judged by many, and under intense pressure at times.)
They are both very demanding professions, especially in the early, "getting established" days, so it might not be wise to pursue both professions simultaneously from a beginning level. However, as many of the above posters have pointed out, you can develop one profession, and incorporate the other into your life as time allows.