Unfortunately, there is no public information about the relative selectivity of different UCB CoE majors at the frosh admission level. At the junior transfer admission level, NE is the least selective of the UCB CoE majors listed at https://www.universityofcalifornia.edu/infocenter/transfers-major .
But note that a 3.8 unweighted GPA is probably around a 4.1 UC-recalculated weighted-capped GPA (see https://rogerhub.com/gpa-calculator-uc/ ), where UCB in general is considered a reach (see https://www.universityofcalifornia.edu/infocenter/freshman-admissions-summary , which shows 13% admit rate to UCB in 2017 for 3.80-4.19 GPA).
Also, there is no financial aid for non-California residents at UCs, except for those who earn rare merit scholarships.