Similar plots that are dealt differently - a spirit/demon that happens to meet a human boy during his childhood years, ends up being his protector/guardian spirit due to certain circumstances in the young boy's life (which involves the death of loved ones)
The only real similarities is how they 'heal' each other. In both mangas one of the characters must be healed from 'something'. One character in each manga has the ability to suck out black substance from their bodies.
I guess the comedy is similar as well, but Silence is, overall, more serious.
I personally think Silence is better. It has more drama and less 'Love/Hate' type of relationships - which Konoyo Ibun has.