So it's possibly a hardware problem. Double-check by running an Ubuntu Live ISO, and see happens with the network speeds.
Great idea. Will try that.
By the way, I've contacted Intel support, and all the first told me was that the NUC didn't had support for Linux. I then told them about my friends NUC, and they asked if I could try my NUC on my friends network, and his NUC on my. Will do that some day.
/Söder