Berkeley was able to make offers to everyone who wanted on-campus housing for second-year students. I can’t imagine that the diff in housing would be $5.5K more per year between Berkeley and UCLA, that doesn’t sound right. The average 1 bedroom in both Berkeley and Westwood is both around $2500 and from what I can tell, dorm rates are the same.
You probably should go to the Berkeley sub-forum and look at the active threads to see some of the similar questions and subsequent answers.