I lived and worked in London (South Kensington/Pimlico at college, Streatham, Walthamstow, Acton Town, Notting Hill - all over, really) for about 16 years. I've been in the Bay Area for ~17 years. There really isn't any comparison. Londoners have it made, even if it doesn't feel it when the train is packed/a few mins late/cancelled.
I see the light-rail here going by on occasion. It's empty. BART is inadequate (there are 270 stations on the tube, there are 50 on BART covering a larger area), and it runs with a 10-20 minute cadence, not the 2-5 minute cadence of the tube. As far as real trains go, Caltrain is pretty good if you're on the track (really, the train itself is nicer than most in the UK) but it's coverage is very limited.
Just like the NHS, you don't know what you have until it's gone.
For many people it comes down to whether they can afford to deposit or get the income multiple loan to buy in the city, not monthly expense.