I grew up in the bay area, so I can speak to Berkeley a little--the environment is going to feel so different than NYC. Berkeley isn't right on top of Oakland or SF, it feels more like an average norcal town than part of the larger city system. I'd guess that cost of living is pretty similar between the two, but Berkeley is a bit more driving heavy (lots of mopeds on campus as well). I think besides of course considerations of which program is the best fit, you should definitely consider what part of the country you want to be in long term! Both areas have a ton of need in terms of social work careers, but cross country moves are a huge ordeal and if you're on either coast, I'd suggest picking the one you could see yourself staying in at least for a few years post MSW. I also visited Berkeley's building for a fellowship interview--it's set in a bucolic little forested corner of campus, and if that is your vibe, it was very pleasant.
If you have or are willing to get a vehicle, Berkeley also encourages you to live anywhere in the area and commute for class, and they'll try to place you with a field placement closer to your housing. For example, I grew up in Napa and they said I could live there if I still had family in the area (10/10 would not suggest commuting from Napa) but looking at American Canyon or Vallejo makes the cost of living look way more manageable. Plus, tuition is way lower since it's public!
I'm definitely biased towards the bay area, but if you've never visited I would highly suggest it! Both are phenomenal schools, I'd just hazard a guess that they feel very, very different from each other.