Although "A Midsummer Night's Dream" by William Shakespeare and "Kubla Khan" by Samuel Taylor Coleridge differ in period and genre, they do have some connections. On the level of differences, Shakespeare's work is a play with multiple characters in which the action is conveyed by mimesis, whereas "Kubla Khan" is a poem narrated in the first person without defined characters or action, but rather is organized as a sequence of perceptions.
The first level of similarity is that they are both written in verse. Both works are set in a magical dream landscape and show visions of things that would have been exotic or mythical to their audiences. They both blend history and myth, with Shakespeare's play using the quasi-historical figures of Theseus and Hippolyta sharing the stage with realistic young lovers and mythic fairies.
Kubla Khan is also an historic figure from medieval China, but the vision contains many fantastic and mythical elements such as the image of the "woman wailing for her demon lover".
Another connection is that Coleridge was an admirer of Shakespeare and was strongly influenced by his poetic techniques.