Is there such thing as a good public school applicant but a bad private school applicant?

I have heard back from a majority of the UC’s and Public Schools I applied to and have gotten only acceptances and 2 deferrals. However, when showing my application stats to others, many said that I do not look good for private schools and my main EC (classical music- Double Bass) would not matter to them. I am not asking for a chance me thread, but mainly wondering if there is such a thing as an applicant looking great to public schools but not good for private schools?
Thanks