Busou Renkin, Kurokami The Animation Recommendations
Both anime begin with male protagonists trying to save a girl only to have a his heart rip apart. They are later saved by the said girl using supernatural means and are dragged into a lot of fights. Both anime are also set in present day world.
Both anime start with a guy being killed while he tries to save a girl with super powers and in exchange of having their lives saved by the girls, they are dragged into a fight to save the human race.
The story line is pretty much the same. They both have lots of fighting scenes and deal with super natural stuff. However I believe Busou Renkin is a much better anime.
Both of the male leads are thrown in a supernatural and known world where battles are being fought for control of the planet. In Busou Renkin it's the homunculus and in Kurokami its the doppeliner system. Both protagonists start off weak and get in the way of the female leads, but as both series progress they both prove to be invaluable partners.
In both of these series, the main heroine helps the protagonist by saving his life. From then on, they become a partner of sorts. There is comedy, action, drama, and even romance later on in the series. Both anime(s) also has more emotional drama as episodes progresses along with various plot holes. Overall, a good idea to keep an eye on both if you're interested in some fantasy and action.