I went through the Berkeley HPM program a couple years ago. Both programs are pretty strong and have good reputations, especially if you want to settle in California. Berkeley may have a little more sway if you want to head out to DC or NYC, but I can't say this for certain.
One potential point of differentiation is that Berkeley's HPM program has ties with the Goldman school and if you want some hard core policy skills, they have an option for an MPH-MPP dual degree. UCLA may have something similar too.
Ultimately, the big difference is WHERE you'll be going to school. Berkeley/Bay Area and SoCal are dramatically different geographically and culturally. You may find that you prefer one over the other, and that may be an important criterion for your choice in school.