Barcelona has some of the best cheap fine dining options, on the other hand. And the quality of meats and things you'd put in a sandwich available in the supermarket is much better for my tastes; I say this as a weekend tripper to Barcelona, I live in London. That makes some sense as most of the population in Barcelona seemed to me to be British expats. By and large I had a tough time finding anything much better than okay (and certainly anything Catalan is well hidden). In contrast I found Madrid to be particularly easy to find good food (and generally less expensive than anything in BCN).
I don't eat sandwiches from stores, last time I did that was 12 years ago. A sandwich is a last, desperate choice. I get my lunch from one of the stalls at a street food market, between £6 and £7.50 every day.
At that price point you've got plenty of options, even in San Francisco or New York. The Yank Sing to-go location downtown is definitely one of the better value propositions.
London is good for Asian food; some of my co-workers who have Asian wives don't think much of the food in Paris for this reason.
The last time I tried Asian food in London was well over a decade ago, but nothing really stood out. Sure, it was better than the chicken and cheese shu mai I had in Spain (let's face it that sounded like a bad idea as soon as those words left my drunken mouth), but that's a low bar.
When comparing things like sandwiches, I think it's important to normalise for sandwich eating as part of the culture.
Sure. San Francisco trends more towards co-opting burritos than sandwiches, but there's still a definite sandwich culture. What we don't have out here at least is any sort of culture around ready-to-go low effort lunch food. In fact I'd say that whole "slow food" movement hit San Francisco particularly hard. At near/under $10 you can find plenty of things for lunch, but you'll probably have to wait for it to be assembled/cooked.