CMU CoE vs UCB Applied Math?

As the title says, I wonder which school may be better for Engineering. As a California student, I would like to stay close to home but prefers to study engineering over math. And what are the chances of transferring from Berkeley’s L&S into College of Engineering (such as Civil or Mechanical Engineering)? Thanks in advance.

as far as I know, transferring to CoE at UCB is difficult to the point where you shouldn’t count on it happening.