There are huge differences in work force that make such comparisons as good as useless.
For example, the jobs for people who put your stuff in paper bags at Walmart do not exist in large parts of Western Europe, and doormen are way rarer. In general, the USA has more low-paying, low productivity jobs than Western Europe. That lowers average productivity for the USA.
Also, measuring productivity is hard. You can't look at pay, as that can be quite different for exactly the same work (you can get a suit made in Asia for peanuts, but that doesn't mean people working there aren't productive)
So, you scale for _something_: average income (before or after taxes), hamburger index, or whatever. In the end, it will be very, very hard, if not impossible, to do that objectively. If the outcome of your procedure differs by a large factor from what you expect, you will search for errors in your logic. If it matches what you expect, it is hard to keep searching as hard.
Is there not some comparison of two similar roles and metrics for those roles? (e.g. an engineering firm in the US produces specs for a bridge in X person-hours vs the Y person-hours it takes a firm in the UK.)
Define 'similar'. Do both firms have to go through the same amount of red tape? If not, is time spent doing extra calculations showing the safety of the bridge productive time or bureacratic overhead?
You _can_ let both design a bridge according to the same rule set, but to measure how hard teams work and not how fast they can do that task, you have to make sure both have equal experience with that rule set (US engineers will likely be faster at designing a U.S. bridge than UK engineers, and vice versa)
To make a truly fair comparison of efficiency of working, you probably will end up with an exercise where both teams design a bridge that will never get built. Possible? Yes, but also expensive.
For example, the jobs for people who put your stuff in paper bags at Walmart do not exist in large parts of Western Europe, and doormen are way rarer. In general, the USA has more low-paying, low productivity jobs than Western Europe. That lowers average productivity for the USA.
Also, measuring productivity is hard. You can't look at pay, as that can be quite different for exactly the same work (you can get a suit made in Asia for peanuts, but that doesn't mean people working there aren't productive)
So, you scale for _something_: average income (before or after taxes), hamburger index, or whatever. In the end, it will be very, very hard, if not impossible, to do that objectively. If the outcome of your procedure differs by a large factor from what you expect, you will search for errors in your logic. If it matches what you expect, it is hard to keep searching as hard.