It is hard to gain admission to UC Berkeley in impacted majors such as engineering. It is hard in non-impacted majors, too. It may be easier, though, than the sub-10%-admission privates, especially since they will consider your achievements in a local context, where you excel.
UC Berkeley will meet all demonstrated need, but will be very generous with self-help first, before resorting to grants. Private schools who meet full need will be more generous with grants.