I have some limited experience of life stateside, having spent 3 years in Nevada while in the RAF, working with the USAF. From our point of view, we worked to UK rules since 99% of the time they seemed safer. I'll give you some general examples; there are of course always exceptions:
Federal OSHA sets standards, not laws, the laws are down to the states, a similar situation exists with Fire Safety and the NFPA. They have codes and standards, but States must implement.
Most states have their own OSHA, some are good, some are useless. While I was in NEvada, Federal OSHA did an investigation of Nevada OSHA
http://www.osha.gov/dcsp/final-nevada-report.html Just read the summary of findings, it's completely Gob-smacking!
I remember a TV report about a death at the construction site for the City Center complex in Las Vegas. It was near the end of the project and it was the 7th death on the site. The News Anchor covered it in about 30 seconds and concluded with words to the effect that 'it was the 7th death but this near the end of the project, it was still well short of the 11 expected by the insurance company covering the site' !!
For a snapshot of labour relations and H&S, see this website by the Carpenter's Union about a major AZ/NV Builder.
OSHA codes and standards are very proscriptive. For example, in working at height they will actually specify the length of the lanyard to be worn.
There is also a 'do it if it's in the book' mentality. I encountered it all the time with the USAF personnel, if the Technical Order has a safety requirement, it was followed religiously but if it was down to thinking for yourself, they couldn't. That may have been a military thing, but I got the impression it was far wider.
If you imagine the worst possible place the UK could go with some of the current government's aims for H&S, then you'll probably find the USA already there waiting to greet us.