Fwiw I live in London and have been to the Bay Area and I think that London is better across all 4 dimensions you mentioned.
Social scene: Don’t know what exactly you are looking for but London is large and diverse.
High cost of living: London is pretty expensive too but cheaper.
Difficulty getting around: London has pretty good public transportation.
Homeless problem: I think I see homeless people 10x less compared to when I was in the Bay.
Fwiw I live in London and have been to the Bay Area and I think that London is better across all 4 dimensions you mentioned.
Social scene: Don’t know what exactly you are looking for but London is large and diverse.
High cost of living: London is pretty expensive too but cheaper.
Difficulty getting around: London has pretty good public transportation.
Homeless problem: I think I see homeless people 10x less compared to when I was in the Bay.