I saw the one in London and I know they tweaked the Broadway version very slightly to make it not so "dark" as the London production. Anyway, if you are going to it, as I was, from just knowing the movie's persective and wanting to see that on stage be prepared to be disappointed. I am not saying that this is a bad thing, it is just a little jarring at first because it has very few elements in it that resemble the movie. I personally enjoyed it very much because it was so different and I thought that it was a great way to melt the book and the movie together.
In regards to the darkness of it, yes, this version is quite dark. Without going into too much detail (I don't want to spoil it for you, unless of course you would like me too) I think that it would easily scare children under the age of 8, even upwards to 10.
So if you have any other questions, just let me know! =D