It's pretty complicated in general. For example, if you have kids, the European advantage tends to be bigger than if you don't (depending on which country, this may include subsidized daycare, cheaper or free college tuition, cheaper or free healthcare, etc.).

In my particular case, when moving from the UK to the US, my estimate is that the "headline" salary number for the US offer I got overstated my pay by about 30% when comparing on a "like for like" basis with the UK salary. It was still a pay increase, but not by as much as you would think from just looking at the two salary numbers.

The main differences were: 1) my UK taxes were lower, 2) the UK job made pension contributions worth about 18% of salary, while the US one didn't, and 3) the US job deducts about 5% of my salary for health insurance premiums.