Kimi wa Meido-sama.

Pretty much a modern rendition of this old work: Weird girls asked to be hired as rich boys' personal maids who live alone. Both maids used to live blood-stained lives. Mostly focus on comedy and daily life. 

Comedies that feature killer assassins moving in to a new family and get used to their new lifestyle. Main difference is that one is just an assassin whereas the other has an assassin, a spy, and mind-reading child living together. Assassins in both shows are very good with assassination-related tasks but are abysmal at chores but one is more energetic whereas the other is very much silent and cold, tho they both have their outbursts of joy in certain moments. 

Both main characters (MCs) have cold-heart/Emotionless. Both MCs possess fighting and weaponry skills. Both MCs have a past as combat tools. Both MCs lack a family background. Both MCs have a sweet yet sharp facial appearance. Both MCs wear very formal clothing. Both MCs want to understand human emotions. Both MCs have innocent and pure hearts. 

- Both series involves a mysterious maid that for some reason just decides to serve a kid - The romance aspect is similar - Both maids have an unknown past that is slowly unfolds on each episode I would say that Kimi wa meido-sama goes a little bit deeper regarding characters story but Saikin Yatotta maid ga ayashi is funnier 

The female protagonists of both series are rather lonely, seemingly cold and distant and lack proper social skills to convey their feelings. The male protagonists of both series are normal teenagers who help them to become confident by treating them as companions.