Honestly I'd say I've had no issues taking BART, but with anything there are always exceptions. I've seen a few incidents on BART that made me uncomfortable, including a clearly mentally ill homeless woman threatening to cut up another passenger. There have been a few instances of teenagers ganging up on passengers and stealing their stuff. This is stuff that can happen on any public transportation system or on the street, so definitely be aware.
I wouldn't necessarily say that the Jack London is that bad, but it's a public place and there's a lot more stuff around there than Emeryville. So there's good stuff there (like the restaurant/bar Plank) but it's also a gathering point for kids with nothing else to do. I'd definitely be aware of my surroundings, especially at night.
The stations at Emeryville and Oakland were built around the same time, but Emeryville is the terminus of the Coast Starlight because of the position of the Oakland rail yard. This won't affect you on the CS, but that's traffic that Emeryville gets that Oakland-JLS doesn't get. They're both reasonably clean, although Emeryville is kind of isolated. There's stuff around there, but it's mostly an industrial neighborhood, although with lots of new multistory residential apartments and condos.
