 If you liked
Mononoke
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 ...then you might like
Noragami
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Both are about Ayakashi (supernatural monsters)
Both have link to traditional Japanese culture (gods, tales etc.)
Both have underlying metaphors/themes for real life problems/situations
Mononoke has unique/rare art style
Noragami focussed more on combat/comedy
Mononoke focussed more on mystery/horror
If you liked the dark & mysterious Ayakashi in Noragami, and you like horror stories, Mononoke will be a fun ride. (For some art style may need some getting used to)
If you liked the dark & creepy Ayakashi in Mononoke, and you like action/comedy stories, Noragami will be an enjoyable ride. (Animation & audio are high quality with great music used throughout)
Spirits that need to be purified, the "fight" scenes are very similar.
They are very different, but they give me the same vibe. Honestly, the give off the same... "maturity", even if noragami is a lot more comedic for everyone.
Honestly, I would recommend Mononoke to a Noragami fan, but I would not recommend Noragami to a Mononoke fan. You choose though.