The best way to understand Denmark from an American perspective would be something like "Imagine if everyone in America was lower-middle class". Whether this is better or worse for you obviously depends on whether you're poor, middle, upper middle or upper class.
For me, Danish culture was something of a nightmare of 'tall poppy syndrome' and bleak, hopelessness that hard work doesn't pay and that no matter what you do, you're stuck eating sack lunches and taking the bus to work because your spouse needs the one car your family can afford. That said, if I had an intellect that limited academic abilities or a more naturally lethargic approach to school and work, I'd certainly find my life more comfortable in Denmark and see the American model as unforgiving.
Basically, Denmark pulls up the bottom towards the median, at the cost of pulling down the top towards the same point, to a far larger degree than the US. Everybody gets just enough, but nobody is allowed to have more than just enough.
They dont celebrate winning like other countries. I totally understand and respect it but it's just not my style. I don't think it brings out the best but I admit it may please more people.
On diversity you are correct. But which individual liberties are Danes lacking? Guns?
Tax rate is certainly high, but it is very much a free-market economy and very business friendly. How do you define high achievement? Living a comfortable and secure life? Getting a college degree? Becoming a billionaire?