I have worked at both St John's and UCLA. I was actually fired from St John's and then picked up an assignment at UCLA. Obviously, I don't feel as if I can recommend St John's. I've been traveling over a decade with great reviews from most every hospital at which I have ever worked. However, my experience at St John's just goes to show you what someone in an authority position can do if they do not like you.
I worked with another traveler that also didn't feel as if St John's treated their travelers well. This was in their ICU, but I cannot speak for other areas of the hospital.
I absolutely LOVED working at UCLA. Now mind you, I worked at UCLA Santa Monica, which is different from the Medical Center. UCLA Santa Monica had close to a dozen travelers when I was there, but I think they have gotten away from using travelers. UCLA main probably still uses quite a few travelers and has many different units to chose from since it is a large teaching facility.
Over the two you gave, I would recommend UCLA. You could also consider Cedars. Hope this helps.