Athletic Mato is excited to start middle school and meet new people, including Yomi, an artistic girl who doesn't open up easily to others. While awkward around each other at first, things change when the girls discover their mutual obsession for a fantastical picture book. But just as the pair becomes fast friends, they're torn apart by a cruel, wheelchair-bound girl who considers Yomi her personal possession and refuses to let anyone else near her. What's worse, Mato has recently begun to have strange dreams about girls brawling in bizarre colorful worlds that seem to parallel her personal struggles. With jealousy, insecurity, and foreboding dreams always getting in the way, can the two girls ever become true friends?
In the not-so-distant future, mankind is at war with itself. The lives of Chise and Shuu are torn apart when Chise is chosen to become the ultimate weapon to fight for Japan against their enemies. Death, sadness, and the hardships of love accompany Sai Kano in its grim look at war and its consequences.
People who enjoyed the drama, action, setting, and overall style of this anime will likely also enjoy Saikano.
Saikano is similar to BRS TV in that it is a dramatic / bittersweet story centering around a "strong" female character, in a similar setting (highschool/post-apocalyptic), and involes a great deal of action / combat.
It differs in many ways, but primarily in that Saikano is targeted at a slightly older age group (contains more mature elements), and that the center theme is romance, instead of friendship.
Vividred Operation is brighter and more lighthearted than Black Rock Shooter, but both come heavy on the meaning of friendship theme, as well as featuring young girls with big superpowers. If you believe in yourself and your friends, you can conquer the world!
They both deal with supernatural dreamlike worlds that can influence the real world and the emotions of people, and they do that by creating a very enigmatic and mysterious atmosphere. Weird and cool fights are also something they share. While Yumekui is a bit more shounen-ish and less serious (and it also lacks a proper ending), I think those who got caught by the style and execution of one of these series will recognize the resemblance and like the other the same way.