Which program do you want to do?
I am under the impression that the Julliard program involves music, at a relatively high level (eg, you need to have been doing this for a while with a significant commitment and ability). Let me know if I am wrong about this.
Music is a tough way to make a living and people who are good at it often actually make a living in a very different type of career. We do have some experience with someone who is very good at music deciding to take a different career path. I will admit that I was disappointed when one daughter gave up on her music to focus on something else (I might have been her biggest fan). However, I understand that she did the right thing. She is now in a career that she loves and that makes a lot of sense for her (she is a veterinarian). I have worked my entire career in high tech but have multiple times seen someone who I know from work get up at a music event and play, and in most cases play very well.
In a similar sense if you are excellent at music, but want to focus on some form of science or math or technology, this is likely to make a lot of sense. I do however see how this can be a tough step to take.
One issue is that you do not have to do either program. Continuing with the Julliard program will show the ability to focus on one goal for a while and reach a high level. Participating in the Columbia science program will help get you started in a direction that you want to go it. You can get into good universities and go on to have a good career in any one of a huge number of STEM fields after doing either one, or even without doing either (although to me they both sound so appealing that I would do one of them for sure if given this choice – picking which one would be hard for me also).
I do not think that you can go wrong with either choice. I think that you should do whichever of these exceptional programs that you want to do. Congratulations on having this choice. You must be doing at least two different things very well!