Bleach, Ga-Rei Recommendations
Both of the main characters have the ability to see spirits, and both of them meet, seemingly by accident, a girl who not only sees spirits but makes it her business to exorcise them.
Bleach and Ga-rei share a very similar aesthetic in regard to both narrative and character design. Both revolve around the constant battle between exorcists/shinigami and the evil spirits that they cross paths with.
If you enjoyed the first arc of bleach but the feeling died once the fighting gone too hardcore for you (second arc onwards), ga-rei might just be your thing.
Male leads can see spirits that other people can't see. This ability causes them to be involved in a supernatural world, and eventually both characters become sword-wielding bad-ass who fights in order to save the world.