Both are "edgy" sword wielding black clad and black haired anti-heroes who are hybrids, technically (Hiei being a child of a fire demon and an ice maiden and Ryuko being a life fiber/human hybrid). They both have rather terrible relationships with their families due to them seeing them as mistakes and even attempting to kill them when they were babies (The villagers called Hiei a cursed child and forced his mother to throw him over the mountain, while Ryuko's mother, Ragyo, called her a failed experiment and attempted to get rid of her after she was born), however they would both actually survive. During their childhoods, they would both join gangs (Hiei was pretty much raised by a gang of thieves where he would murder everyone, while Ryuko became a juvenile delinquent, constantly getting into fights and even going so far as to join a gang). Their main goals in their series are heavily tied to their family members (Hiei wanting to find his sister, Yukina and Ryuko wanting to find a killer of her father, Isshin Matoi and avenge him). Speaking about sisters, both have lost white clad sisters (Yukina and Satsuki), who weren't even aware of them being their siblings. Both were subjected to experimental enhancements that soon greatly changed their bodies so they can become much more deadly (Hiei received the Jagan implant and Ryuko's body was fused with life fibers). They both have powerful strenght-increasing forms that they can achieve through their jagan/life fiber abilities (Jaganshi, which is an ability that jagan users can use and Senketsu Kisaragi, which can be used by Ryuko through absorbing the Life Fibers of Goku Uniforms). Both are also much more serious compared to the rest of their shows' casts.
Not exactly the most thematchic Ryuko MU but I haven't seen anything better for Hiei