UCLA or UC Berkeley?

Yes CAL is very competitive. Have you visited?
Yes LA is competitive. Have you visited?. It does make a difference if you visit the campuses; you can feel it.

My daughter attended UCSF for pharmacy from UCD.
Most of her classmates at SF were not from the UCs; they were from every other school in the country-small privates and public colleges.

For UCSF housing, all of the students are integrated together. Her roommates were medical students. Most of the students weren’t undergrads from Berkeley or the other UCs.

My neighbor is on the UCSD med school interview panel. Most of what she’s told me is that UCSD knows what their students are doing, but they’re curious as to the experiences of what other schools, in other parts of the country, are doing in medical research and practice. They wipe the slate clean and look at what the student has done. Being from a UC is not prioritized, or an advantage. They like to get a variety of students, who have done a variety of things, as they build their classes. They start from scratch and read the application, GPAs, MCAT scores and the student experiences.

Going to a UC will not guarantee admission into a UC med program. This is why your undergrad experience has to be something that you will enjoy and thrive.
You really do need to visit the campuses of the schools because you will live there for four years. If you make a decision and you never visited, then that will be on you if you don’t, at least, enjoy the experience.