Even if your child was OK with the movie, it is a good idea to be wary about the book, as it does explicitly state that the Other Mother steals souls, not just eyes (a very scary theme, especially for older children who understand the concept of souls and religious families who are not happy with the idea of young children losing their souls) and it does describe the Other Mother's tortures in a lot more detail in the book.
However, I read this book when I was eleven, and, although I agreed that it was a very scary book, it was not gory and not horrific. In fact, I actually loved the fact it didn't shove gore in your face - it was mature, genuinely creepy stuff.
There is a positive message in the book that was completely ignored in the movie version - they morphed it into another 'be careful what you wish for' film as opposed to the real point it was trying to get across - that sometimes, when life is hard, you have to do things yourself. I have no idea why they decided that they had to completely remove this moral from the movie and replace it with one that has been explained enough in children's TV and movies and is by far much less relevant to real life.
My final warning is that, if you decide to read this as an adult, then there are a few things you may pick up on that I, when I was eleven, noticed were probably going to terrify adult readers. Messages like 'if you don't pay attention to your child, they'll run away' and 'remember parents - kidnappers are everywhere, even in your own home'.
And yes, now I am terrified of buttons (kompounophobia)