At the high school level, I do not think you need to worry about career direction with this decision. Juilliard prep grads often get into top colleges. If you applied to BS programs in STEM, you would do a music supplement with recording/video, music resume and 1-2 letters of recommendation related to music.
Continuing Juilliard vs starting the science honors program, in other words, is not likely to affect admissions chances, which are relatively high with that level of music. So if that is what you enjoy most, do that. Would you miss Juilliard?
On the other hand, if you absolutely love science, and are ready to give up Juilliard prep, do that. If admissions chances are not your focus, but instead your current interest level, then do what interests you most and gives you the most enjoyment.
I have a kid with a PhD in music. But doing Juilliard prep does not mean you are headed for a career in music or even a major in music. You will be most welcome at many campuses for extracurricular music while you pursue STEM.
I suppose an argument could be made that sticking with Juilliard shows a depth of commitment. Then again, doing science shows commitment to that. Basically, again, what do you actually want to do without regard to admission to college, or future career? Because at your age that should be the deciding factor- what you want to do.