How good is he at math? Math degrees are one of the subjects where the long tail of talent is very long and very obvious. IMO (I did undergrad math then a PhD in a subfield of engineering, my first job was computer programming) for a good hard working student who isn’t a superstar it is easier (and usually more satisfying) to be in engineering than math. On the other hand, an extremely talented mathematician will find that degree easier (and more fun) than engineering.
That difference will be more obvious when comparing UCB math (which will attract some very talented mathematicians) with UCSC engineering (which has strong students but fewer superstars).