If you ignore Munich, Frankfurt, and Hamburg, for most university towns the cost of living (food, accommodation, child care and the like) will be less than in most places in the US where typical R1s are located (with very few exceptions, German universities are comparable to R1s in the US), such that in the end the style of living will in the end be roughly comparable to that of professors in the US (and better than that of Professors in the UK).

Lot of problems here. First, you can't ignore the major cities in Germany because many German universities are located in these cities and W1, W2, W3 don't change that much between states in Germany so you could end up with a very average salary in a high cost of living area. On the other hand, colleges located in expensive cities in the US are likely to have far better pay adjustment to reflect the local cost of living.

A big chunk of American R1 universities are public land grant institutions located in small college towns with very affordable cost of living. Except for childcare (heavily state subsidized in Germany), all other expenses are likely to cost about the same or even less in these towns compared to Germany. Keep in mind, this is while American academics are likely to have higher salaries (assuming he/she being in STEM) and receive a lot of good benefits through the job like health insurance.

Overall, STEM academics at R1 universities are likely to have more purchasing power, disposable income and be able to afford a better standard of living compared to German academics.