Both have that unique combination of making you feel happy, sad, confused, empty, overwhelmed, and captivated at once.
Both have multiple couples with Goblin having 2 and More Than Blue having 3.
Both depict the power of true love and what people will sacrifice for the person they love the most.
Both have beautiful OST’s
Both involve working in a music setting- (record company for More Than Blue and radio station for Goblin).
Both have great performances
Both will stay in your mind for a long time after you have finished.

Both have warm and bright female leads
Both have male leads with a visual impairment
Both are love stories that have an artistic foundation
Lovers of the Red sky the FL is a painter and in Crush ML is a songwriter
Both have leads that are known for good acting
If you like these elements in one check out the other!

Both have lawyer couple main leads and involve taking down a big corporation.
Both have similar action scenes and court scenes.
Both have a male lead with a troubled past.
They have a similar tone and sense of humor so if you like one you should try the other

Both have immortal, smart, powerful, sassy (also well-dressed) ladies as the lead and unknowing male leads that get pulled into their world . Both series have paranormal aspects and a woman trying to recover memories about her past. Both love stories also develop similarly with the woman commanding the man around but then unknowingly falling in love with them instead. I think if you like one you will most likely like the other one too!