The words EECS and CSE can be misleading. You should look at the specific course requirements of each school.
At UCB, EECS has 2 majors: ECE (more hardware), CSE (more software)
http://www.eecs.berkeley.edu/Programs/ee+cs.html
At UCLA, there are 2 majors: CSE (hardware and software), CS (software)
http://cis.ucla.edu/studyArea/course.asp?id=74
http://www.seasoasa.ucla.edu/curric-14-15/28curcomscieng-14.html
http://www.seasoasa.ucla.edu/curric-14-15/27curcomsci-14.html
At UCSD CSE has CE (hardware and software) and CS (software)
UCSD ECE is hardware only.
http://www.cse.ucsd.edu/node/35
http://www.ucsd.edu/catalog/courses/ECE.html
What do you want to concentrate on: hardware or software?
Why your parents say UCLA CSE is weak?