You're moving the goalposts a little with the vacation issue, but fair enough -- although (a) 5 weeks vs. 3 isn't a night-or-day difference and (b) I can tell you from personal experience that it's almost always possible to negotiate a better vacation policy, especially if you're willing to pay a little for it. And let's be honest: whether or not a vacation jeopardizes your job or career is something that you have a LOT more control over than your post would suggest (unless you're pushing the skill, performance, age or compensation boundaries of your role).
More importantly you're missing my main point, which is that it's not a 12% difference like you suggest. It's more like a 15-17% difference in take-home pay (between lower gross salary and higher income tax) AND everything costs (at least) 15% more, so each dollar you do earn is essentially worth $0.87 or less. In other words, the actual difference is more like 25% at the low end.
The reason you haven't seen anything demonstrating that European health care isn't a net savings despite higher taxes is that almost no such comparison presents a complete picture of the taxation differences. Most merely compare one dimension (income tax) without accounting for sales tax (25% vs. ~9% -- and BTW since you brought up regressive, VAT is about as regressive as taxes get), capital gains tax (28-42% vs. 15%), etc. or the difference in average gross pay for the same work (~$10k).
Nevertheless, let's be charitable. Out of the 25% or better premium that Danes pay over Americans, let's allow that 15% goes to health care and the additional vacation time. Mind you, that actually means that the difference in gross wages is really substantially greater than $10k, because employers aren't paying for health coverage -- but let's even let that go. We're now left with a 10% overage that you're paying for life as a western European.
Since the original thread is about paying for education, note that while your 4-8 years of college may be subsidized, you are paying that 10 cents out of every dollar for it for your whole working life. It's a rare American student who can claim to be saddled with such a burden of repayment for his education.