I can't speak specifically to the comparison of Berkley and Davis, but I do have some perspective on the general question of choosing between an elite school and one with less prestige.
A couple years ago I got into an argument on another forum with someone who insisted that an undergrad degree from MIT made a huge difference compared to a good smaller, but lesser known school (Harvey Mudd) that attracted similarly qualified students. I dug up some salary studies comparing MIT, Harvey Mudd, and a number of other engineering schools, and what do you know, the difference between Mudd and MIT was minor in early, mid and late career.
A study of people admitted to elite colleges across disciplines found that, pretty much universally, people who made the cut for an elite school, but ended up attending a less elite school for some reason, did as well in their working life as the graduates of those elite colleges. The exception was people from poorer families, often first in their family to go to college. In that group, the elite schools seemed to provide an advantage.
Its certainly true that some hiring managers will give you more consideration because you went to Berkley, and there may be other advantages, but that isn't the whole story. One obvious difference is that Davis is going to cost you less money. That could mean less time working, more time for studying and working on projects with your peers. It could mean substantially less debt at graduation, and therefore more flexibility about the jobs you take in your first 5-10 years after school.
Oh, also, consider that a hiring manager that skips over a well qualified grad from a lesser school for one from a top school because he/she finds it easier to justify may well be the kind of manager who can't defend their staff against unreasonable schedules, budgets, requirements (ie, a terrible manager to work for).
Congratulations on your acceptances! It's good to have choices.
I can't answer your question for engineering. But in the academic and basic science research world, university pedigree does play a role at the graduate school level and beyond. Undergrad not so much.
True, but not universally, particularly in this era. A friend from undergrad went to a second tier research university for his life science PhD, and now has a nice lab at a top-tier research university. In his telling, at the second tier university, he had the chance to learn how to be a researcher -- design experiments, write grants, take the lead on papers, the whole ball of wax. At a top tier university, he would have been a cog in a machine. As a result of his choice, he was able to build his career at a time when so many PhDs are having trouble even scoring a job in academic research.