So all of Norway (rural and urban areas together) had a higher per-capita rate of bike theft than New York City (which is all urban).
[1] http://www.sykkeltyveri.no/bicycle_theft.html [2] https://www.bicyclehabitat.com/articles/security-pg80.htm
The size of the city isn't the issue here. There is definately a correlation between size and crime, but that's not the real issue - what it is I don't know though.
I live in a mid-sized European capital (bigger than Lisbon), and it's one of the safest places I've ever lived. I could probably leave my car running, with an expensive camera on the dash, while going to get a coffee, and everything would still be there when I get back.
Compare this to some Italian cities I've been to - which are smaller - where I feel lucky all four wheels are still there when getting back (locking wheel nuts are easy to break btw). I lived in Rome for a while and if you left something that even looked like it could contain valuables on show, you'd come back to a broken window.
Locked bikes are stolen in broad daylight in front of grocery stores and at schools. It's probably not as bad as SF, but it is still an issue in the suburbs.
In non-urban areas in the US things are better for sure, but you still have to deal with other things like having complete asshole neighbors that you really can't do anything about because small quality of life crimes like partying every night with loud music is not a crime.
If you move to rural areas this goes down even further, but then you give up a lot of amenities.