When I first saw the two websites images above I thought the only thing alike between the two is they both use black and white photos. However, when I visited the two websites, I did find the proportion of the color blocks are similar also. Besides these, I do not see other similarities.
There are so many websites with similar colors, compositions, layouts...; it's really hard to say nowadays which one copies others unless the two sites are completely and EXACTLY the same. There are some real web pirates who download others' sites completely, only change the text and put on the internet as their own website. This is what I called a crime. And I've seen a couple of them.
Think about it, can Barns & Noble.com and Amazon.com sue each other for similar website layout? Or can Yahoo.com sue all the other website for using same layout?
There are so many common layouts which later become templates. I'm sure the Swedish firm Made In Sthlm is not the first site to use the composition and Crown Prince Frederick's website would not be the last one to use the layout either.
In Andy Warhol's portrait series, he didn't take all the pictures of those celebrities. But he did change the colors and use different medias to present. Thus they were his works and new creations. No one can sue him for copy. Even some of the photographers are happy their works being reproduced in such a creative way. That's how things work in art field. A line or a color change makes big differences.
Here are two photos of Hillary Clinton and Princess Diana which I found alike. I wouldn't call it copy but ... inspired maybe.
Back to the topic, only the designer of Crown Prince Frederick's website knows if he gets inspiration from the Swedish website. No matter what the truth is, both sites have already got enough publicity.