At UCSB there is usually going to be one offering each quarter for the required ME classes so the enrollment will be the size of the ME class, generally 75 or so according to degrees awarded [ Degrees Conferred | Office of Budget & Planning and look just at ME degrees] For ME electives the class size will be smaller since not all students are interested in the same electives. At a UC the lecture will be by a prof, labs and discussion section run by a TA. For lower division prep classes (physics, calculus, etc) those are going to be larger than the ME classes.
At a CSU classes are going to be smaller right from the start. The tradeoff, though, is that CSU hires lots of part-time adjuncts. Since the number of MEs per class year isn’t huge most ME classes will be taught by fulltime faculty, but those small prep classes (physics, calculus, etc) are often going to be taught by lecturers. See for example Mathematics & Statistics and look at the faculty listings.
Both are ABET programs and will do a fine job of teaching ME. There are some differences in class size but IMO the most important factors affecting student outcome are how hard the student works to master challenging subjects and whether they get internships.