Quality of life has few objective measures beyond standard of living. One man’s “quality of life” is another man’s oppressive conformity and risk averseness. American culture places an enormous value on self-actualization and trades comfort and certainty to get it. Average Europeans demonstrably would not make this trade in many cases. Neither is objectively correct.
I think Europe may have had a comparable or better quality of life at one time allowing for the cultural differences. As someone who has spent a lot of time on both sides of the Atlantic, I don’t think that has been true for well over a decade. The slow impoverishment of Europe has become noticeable to American eyes in a way it wasn’t before.