Just read the Shiki manga, have a few thoughts about it.
Overall, I was very surprised by how faithful the anime was to the manga - almost everything was identical. Whilst I usually believe manga versions to be superior, though, in this case I think I actually prefer the anime, which is very rare for me. I believe manga, in most cases, to have better pacing and be more mature, but to be honest I thought the manga went a little quick in places whereas the anime had perfect pacing, enhancing the creepy and unsettling aspect of Shiki but still allowing good character progression and frustrating many cliffhangers.
Not only that did the anime stay faithful but it also added a few scenes in here and there which I actually think enhance the story-telling - one problem I found with the manga was that it lacked showing the human side of Shiki's compared to the anime due to less time focusing on them as a whole. There is only two chapters as well that haven't been made into an anime so I suspect they will release them as OVAs or DVD extras as it is literally 1-2 episodes max.
There is so little difference I don't think it matters whether you read the manga or watch the anime, but if you watched the anime then read the last 2-3 chapters to get closure on the story.
Overall:
anime - 4.5/5
manga - 4/5