Danish original and this USA remake.. Spoilers
This was almost an entire replica of the Danish movie with very small differences.
If you haven't seen either one and are trying to decide, watch the original and stop reading this. I watched both because I like Jake G.
The main difference was, in the American remake it is revealed that the baby is alive at the hospital. In the original, the officer who was at the house clearly sees and makes it obvious that the baby was not alive.
This difference is probably because American audiences cannot stomach a mutilated dead baby, even though that aspect makes the story more tense and dark.
The second difference was not in the detail but the ending montage with news audio stating the main character pleads guilty in his court case. In the original, the ending implies that he has a turn-around of conscience. In the US version, because we are dumb, it has to be made explicit to us.