The resources you’ll have at MIT, as a private universities, simply can’t compare with what you’ll find at Cal for undergrad. For instance, MIT has this program where they pay you to go abroad and live at a school where you get to demonstrate your research and a hands-on project of your own design. If you want an internship, they will help you in every possible way, and the interns’ salaries are pretty sweet. You can switch majors easily, or double major, or create your own. If there are too many students for a class they just open a new one instead of making you wait a semester more till you can take it. There are labs where you collaborate with industry projects or are provided material to invent stuff (you can apply and not only is your material paid for but you get a stipend). In terms of prestige they may be equivalent but prestige should be the least important criterion; in terms of experience a wealthy private school is very unlike a public university no matter how good the public university is. There are resources and programs there you won’t even know exist if you don’t attend.
So, my recommendation is MIT for undergrad and Cal for grad school (funded).