Violet Evergarden, Mahoutsukai no Yome Recommendations
-Both show themes of learning about emotions, and coming to understand feelings.
-Both can make you smile, both can make you cry
-Both have an interesting world
-Though this one applies more to Violet Evergarden in my opinion, but both have breathtaking animation
-Both have great music
-Both have an episodic storyline
I am not sure which show should I put as the recommended one, seeing that both shows are already popular in their respective seasons.
Now then, onto the most similar part of these two shows - the process of emotion learning. Both protagonists (Elias from Mahoutsukai, and Violet Evergarden the titular character) have went through a messed up past, causing them to lose the ability to act as humans, and sense emotions. Both shows set up episodic parts and through the interaction of many other characters, our protagonists gradually learn these emotions, often in some sort of heartwarming tales.
Animation wise, both are top notch, we have
-Both have gorgeous artworks
-Both having a young girl as the main character
-Both have beautiful soundtracks
-Both have good story line
The difference being, Violet Evergarden is more related to real life and shorter compared to The Ancient Magus' Bride.
Both are episodic dramatic stories about a girl who has had traumatic experiences in the past and builds emotional connections and more confidence in herself as the show continues. A very emotional vibe to each episode, and a Slice of Life vibe. Both series are very pretty to look at but lack substance or good writing or pacing.
Both lead charters had really hard past and having a hard time dealing with emotion and generally connect with people and world around them.
Both have beautiful art
Both have similar plot that dealt with being not accepted by society
Both have similar episodic narrative
Both deal with the lost of love one
Both have main character learning new things to adapt their surroundings
In short, Mahoutsukai is a narrative driven story with a beautiful plot i, Violet evergarden instead takes you to a feel trip that can make you cry.