For me, half of the appeal of watching Broadchurch is in seeing David Tenant play a different role than the 10th Doctor. Luther is pretty dark. It's well done and has interesting characters, but it is a little much. Sherlock was great (I'm still waiting for more). In my opinion, the BBC Sherlock is better than Elementary.
There's some good stuff there. In addition, a British series (or "season" in the colonies) often lasts for about six episodes. As an American viewer, watching a series end just as you're beginning to enjoy it is a bit frustrating. We're used to getting approximately three to four times that number of episodes per year. Of course, one could argue that the reason British shows seem so well done in comparison to their American counterparts is the fact that they take more time to produce.
One could also argue that it has more to do with the number of working brain cells in Hollywood.