Private vs. Public - which one is more competitive?

[BloodSweatTears, CNA]

Hello,

I am curious which one is more competitive; Private vs. Public.

Of course, I believe non-prestigious private is a lot easier to get in, but what about prestigious private school vs. prestigious public? 

I am applying to only public, cause private is a way too expensive. I am worried public would be more competitive. Of course I know it depends on the region, cohort, and all other different factors. Im just curious about what most of people think.