The reality with health System, true story from a person who is expat from 2008 paying over 50% in taxes since came here in Denmark.
I know every experience is different so might not be all over Denmark the same, but here is my story.
Came from Texas (where by the way got an excellent medical service due to my husband聮s insurance with a big company) before that lived 7 years in Canada (very nice services, longer waiting list but still reasonable, just to mention that Canada is having maybe maxim 45% taxes, same national system like here in Denmark).
All in all we are paying a lots of money for very lousy services when you need them, meaning when you have to investigate a problem like myself. Can not receive a CT scan or MRI, long list, no reason to get one ... I was told.
My firs:t experience with the doctor was when being allergic to the most common hormone prescribed in Denmark to the point of having high blood pressure and frozen lips I searched myself and print out from the internet a page from a website and show her that she can prescribe for me a different brand because is not anymore under special request process.
Second experience: After travelling to Spain I started having problem with my stomach, like any normal person you believe that you got a friendly bug

On 30'st March 2011 went to doctor, and complained that I have a lot of gas, burping, foul smell, my back is burning (and she told me she never heard about that) did blood test, 1 stool test (negative);after few weeks I told her that now my burning is upper and I am having acid in the mouth, and asked to check for Helicobacter test. Received one, got treatment for it. After the treatment the burning was 10 times stronger. On 31 Aug, done a quick endoscopy 3 minutes of vomiting on the table, no sedative, spray or anything else, 10 minutes all the appointment (private clinic), diagnostic of Hiatal Hernia, reflux, got medication, found no Helicobacter. After the prescribed period I am off medication again, feeling good for maxim two months....and again I do not know what to do. Desperate I am doing with Metametrix (expensive lab USA, a test on my own 500usd) and going back to the doctor, she cannot read my results and is sending me to another specialist this time a gastro-nutritionist. Never ever in my life I have seen such a medical place, not dirty but old in appearance, dark and gloomy look,veterinary clinic聮s looks better in USA. At least he was for 30 minutes listening to my story but frugal looking into my expensive lab test, he is mentioning that I can do few more tests and a half colonoscopy right in his medical facilities (EXCUSE ME? no way I do that test there) the place looks in such a way that if you take out the medical things there and create an archive of books will not notice a difference. All other tests came normal, he said I prob. have IBS. Here we reach already Feb 2012, and I would have accepted all the diagnostics but my teenage daughter is starting having stomach problems also...so I insisted to say that might be something common? After travelling? And now I passed into her! I was told that no reason for Helicobacter but they can perform just one stool test, for parasites (limited budget). I said usually you need 3 of this on a spaced interval; sorry this is the protocol in Denmark. I offered to pay for it...was refused. After seeing the doctor one more time she said that my daughter is probably having IBS and needs to do a colonoscopy to confirm that. Just to mention that she is burping many times a day and having change in the stools. IBS with burping? Never heard before, giardia or Helicobacter? Maybe ...my experience with doctors is bad, maybe for Danish people is different but for us, expats, even with maxim taxation, is bad!
Here I am today 31 March one year after my first appointment, self medicating myself with the ppi dosage since nobody seems to give a proper advise or care.
Third experience: With a constant pain on the left side; have seen a gyno, did an ultra-sound and Recommended to me to "reasess the pain since is part of life";
All in all I was paying out of my pocket more than 3000 usd in Chiropractor, acupuncturist, homeopath treatment to fix my problem or be better until our time for leaving Denmark is to come.
My recommendation 聳 If you know that yo do not need any services at all, it is ok to come if you want, need and convenient, money wise, travel, new experience, but if you do require services - GO and work in a different country! Because you pay high taxes for no services.