In regards to the "crazies" aspect: I've spent a few months in SF (near Haight St), and 5 years in London.
The thing that shocked me most about SF was the shear number of mentally ill homeless people on the street. London has homeless people, but they're generally coherent enough to carry on a conversation. In SF it seemed that almost 100% of the homeless were "bat shit crazy" - I pondered at the time if the NHS's mental health care was the difference, and thanked good fortune to have lived my life within countries with social care.
An old guy collapsed on the street in front of me in London. I thought he was a drunk tramp, but my sister (who lives there) immediately stopped to check on him as did several other passers by. Turned out he was having a heart attack. Someone with medical training came forward and pumped his chest cavity or whatever they do while we ordered and flagged down the ambulance.
Guy was conscious but confused when the medics arrived.
Nobody urinated on him or stole his wallet. Anecdotal evidence that suggests were you really on fire people would do more than get out the marshmallows.
And conversely I saw someone get stabbed in the stomach at Waterloo. I was the only person out of at least 200 witnesses who did a thing and to be honest I have no idea what to do so could only apply pressure and call paramedics.
Same with an old woman I saw faceplant on the pavement. I was on a bus that was moving. People just stepped over her.
The worst thing: a guy got pushed in front of a friend's tube train (he was a tube driver). Immediately after he got out of the cab, some platform peon started shouting at him saying "how fucking long is this going to take?". The guy was pretty much screaming his head off on the track under the train dying painfully and slowly.
Good for that heart attack guy, but he must have been lucky. It isn't the norm - and the police I've spoken to over the years confirmed it.
Yeah, I'd agree with that. I've lived in both. This is not to say that parts of London aren't dodgy, but SF is I think both subjectively and quantifiably worse.
For example, London has around 500 people sleeping rough each night. San Francisco has almost ten times as many, between 3-5,000 (mainly because a winter's night in SF is rather more survivable than a London one).
More subjectively, I think public transport in London far surpasses SF, both in terms of safety and quality (...Friday nights excepted, but I think that's par the course of any large city).
Expensive: check. Bad schools: check. Disfunctional government: check. Drugs on streets: check. Lots of crazies: check.
The thing I hate is that people wouldn't piss on you if you were on fire.
Going to move out to the countryside I think...
As for the nutter on BART, I got urinated on whilst on the tube in London .... twice. And no I was not on fire :)