Both anime start with what seems to be a chick going crazy and killing people with what seems to be telekinetic abilities. From there the story progresses into the personal struggles and issues with these girls, whilst also investigating what happened to them in the past. If you like one for its investigative story and excessive level or gore and nudity you’ll be sure to like the other.
Artwork in both anime have great resemblances, due to the fact that both stories are written by Type-Moon. These anime feature a world where magic exists, and can be used be a given few people. Furthermore, the female protagonists are sword/knife-wielding bad-ass without descending into the usual dere stereotypes.
Most people think that Higurashi is a violent anime. But I think Kara no Kyoukai is even more so. While Kara no Kyoukai's plot development is not as strong as Higurashi's, it offers better action scenes with good graphics and an even better soundtrack. Both are high quality anime.
Grossly dark but entertaining story's with murderers that are beyond understanding; In Kara no Kyoukai 3 Fujino Asagami and in Psycho Pass Rikako Ouryou among other people.
Both got action and mystery.
Both feature main female heroines with supernatural powers who fight enemies that are somehow related to the source of their own powers.
Both have a regular male companion to their adventures.
Both have a dense and dark feel to it.
Art is similar.