It's certainly true that Europeans take more vacations and spend more time abroad. They also win on spending less time at work and more time with their loved ones.
Those weren’t the claims the grandparent made. Europeans do work less and vacation more often, but even when you account for this, they still earn less per hour worked.
Vacation time itself might be a good metric for quality of life (which I am not disputing is probably comparable if not better in Europe if you discount the importance of material wealth), but time abroad is not since Americans have access to a lot more variety within America than a European would have within their own country; it’s the same reason more Europeans have passports.