Onikirimaru

Both Devil May Cry and Ogre Slayer follows a main character that hunts and kills demons with an incredibly powerful sword. The main character (Dante and Onikirimaru) in both anime lose someone very important to them at a young age and must protect the humans that they encounter. They are also action-packed anime with a dark and gritty atmosphere. They also contain similar levels of violence, blood and gore. The main difference between them is that Ogre Slayer is short to watch and is way older while Devil May Cry has more episodes and is more recent. If you like one, you may like the other. read more 

SD, like Teito Monogatari, mixes a slight bit of history (in SD mythology is more prominent) along fiction that is built on top of it, and like Onikirimaru it inserts interpersonal drama that juxtaposes the existence of oni along others' lives, although they are more verbal than the ones in the latter series, and at a couple of junctures they even display sadness which oni aren't typically associated with. 

Most of Onikirimaru's manga wasn't seemingly animated, though what remains still complements Youma's atmosphere. 

Both anime take place in a modern gritty urban setting with the main character hunting down demons. Both anime feature characters slaughtering demons with their swords and both are also pretty gorey too. They have enough action to keep you entertained. 

In Onikirimaru, the MC goes around slaying oni while in Mononoke, the MC deals with all types of ayakashi/demons. Onikimaru looks like your typical 90's gorefest horror but with an episodic format, and Mononoke handles its horror with a unique, experimental art style. Besides the few short arcs in Mononoke, both are episodic and can be watched in any order without prior knowledge of the show. On top of that both MCs are not human and don't seem to age as they go on to the next incident so by the transition to the end of each episode it creates a similar bittersweet feeling knowing more is to come. read more 

Similar character design and demons near a school. But Ogre Slayer's more drama, less action.  

The main protagonist in both titles wields a powerful weapon and battles various demonic monsters. They both fight in the name of justice by killing demons with gruesome attacks while the world that they live in is plagued by mayhem. They also have a lot of action, violence, blood and gore. The biggest difference between the two is that they are set in different time periods (Ogre Slayer is set in a modern day world while Berserk is set in a medieval setting). If you enjoyed one, you will enjoy the other.