They are similar because it is about time traveling and in the king is not easy they switched souls and, in the dreaming back to Qing Dynasty is the same , but in here they lost memory of their beloved one (of each other). both Dramas also wanted to find a way to resolve this.
Both drama are Historical , comedy and kinda supernatural.
King is not Easy it's about bodyswapp in a mysterious way
Let's shake it is about an alien which takes a human body