Both are supernatural horror series based in a small, somewhat isolated town with an unusual and dangerous secret. Incidentally, both series are based on novels, and the original authors are married; though these series approach fairly different subjects, the similarities in their styles and tastes are clear.
In both manga, there are people that aren't allowed to exist because they may be a threat to the others. It is discussed the moral problem of killing a murderer and there are also twists and smart moves. There are complex characters, well psychological analyzed and some of them show their madness and obsessions. While Shiki is a supranatural and horror manga, Spiral is a mystery manga and it also has a more optimistic atmosphere and less gore. However, both express deep feelings and they manage to shock the readers.
In both series death is taking place left and right. In one, the deaths are thought to be natural or maybe some kind of illness. In the other, they are all thought to be suicides. both are interesting and unique and have horror =D
Although not the same, there are striking structural similarities. Mirai Nikki has a protagonist who recieves an empowering item that puts him at great risk and requires him to forge alliances and take arms against others within a similarly affected group, with his survival primarily dependent on knowing who to trust and when to trust them. Shiki is about a group of protagonists, some of whom become supernaturally afflicted, whose survival is dependent on knowing who to trust as the death toll climbs. Not the same, but similar.