In terms of quality -- it's totally fine. You'll be taking the Red line or the Orange line if you're headed to Berkeley from Oakland and generally speaking a far amount of people clear out at Oakland so it'll never be super crowded. On the way back, you'll always get a seat too unless it's really peak hours, in which case you'll stand, but the trip takes 15-20 minutes max (the BART part). Campus is a 5 minute walk from the station, but depending on where you have to get on campus it can take up to 30 minutes walking when you get on campus. Luckily during the year there are shuttles that will stop near the BART station. Those shuttles are free to students.
I'd say the only complaints are that BART doesn't have nearly as many stops as it should considering it's usage, which applies everywhere (even in SF). Secondly, BART does shut down at like 1 AM or something, so if you have to stay really late on campus then you need to find an alternate. After 8 PM service is pretty sporadic too, but the longest you'll wait is 20 minutes or so. So, make sure to time your trips a bit if possible.
I mean aside from that BART is kinda grimy, but I mean, it's public transit in the United States.
I dunno man. BART is uniquely not great over other mass transit systems. And I think that's because of how much distance BART has to cover, and not having the funding to keep up with growth and capital investment. That's not BART's fault, that's just someone doing some poor urban planning and BART not getting the money it needs to adequately serve its customers.
Chicago has its problems. But, that trains are in better shape than most US cities I've been to. CTA's issue mostly have to deal with being very hard to put in new stops anywhere without making major adjustments to the city. The big north/south line is expanding here and the city had to eminent domain 2 city blocks in a busy area of town.
NYC. I think it's far more comprehensive of a mass transit service than any place I've been. But, it is also the most down shit heap of public transit I've ever seen.