I think the biggest driver here will be the ability to procure housing. Seattle has much better options. I own a one bedroom in SF, and it rents in the mid 3000s, and that’s a fair price for the neighborhood. Conversely, I just help rent a place for neice who is in grad school, and she got a nice 2 bed place in Portage Bay, at 2000, which is like 6-7 minutes from Udub and downtown.
^^^To be sure the SF bay area is outrageously expensive, but remember where the OP is coming from.
If the object is to have a lot of fun I’d pick Berkeley for sure simply because of the weather. Seattle gets roughly twice as much rain as Berkeley annually. Plus in my experience with Seattle there are a lot of winter days and weeks that might not have all that much rain but are still socked in with dreary overcast.
When it comes to fun in the sun, Berkeley is not San Diego, but on the other end of the scale it’s not Seattle either.
Annual average rainfall in Seattle is 34.1 inches, while in Berkeley it is 26.75 inches, according to the “usclimatedata” website. However, as Scipio notes, Seattle gets at least twice as many “days with precipitation” (i.e., drizzly mist). Wherever you decide, you should take a long weekend trip to the other for fun.