I was a little concerned about the area as well. My daughter was raised in a very safe area. I went out to visit with her during Explore USC and thought the “scary” description was a little overblown.
In some ways, USC feels more safe then other schools we visited. USC, because they want to ensure a safe campus, has paid more attention to possible issues than other colleges. My daughter walks back and forth to the sorority house and I asked her if it was safe. She told me she always is in sight of USC security during her route.
USC also provides free Uber or Lyft within two miles of campus (I believe). It is always prudent to remain alert and aware but I think that’s true anywhere. I’ve seen other posts that actually have UCLA one spot behind USC in campus safety/crimes reported. I haven’t looked it up to confirm that but it doesn’t sound like it’s as bad at USC as it’s made out to be.
The difference in private vs public can be significant. UCLA has a wonderful academic reputation but I think the graduate schools play a big part in that reputation. I’m sure they have an outstanding undergraduate experience as well. I have read that it can be very difficult to get all your classes as a UCLA undergrad, even to the point that a fifth year is sometimes required. For undergraduate experience, I think USC would be the better choice.
One of the things that clinched it for my daughter is the outstanding Neuroscience and Philosophy programs at USC. USC is doing a lot in Neuroscience and their Philosophy is now top ten in the world. Your selection of major may also be something to consider when looking at both schools.