Arkham Asylum: A Serious House On Serious Earth (1989) is an original graphic novel by writer Grant Morrison and artist Dave McKean. It is primarily a story examining Batman’s psyche by showing him facing deconstructed versions of his foes. These examinations of his foes also give brief explanations of why certain methods to cure their psyches will not work. An example of this is how Two-Face having his coin replaced by other objects that represent more possibility causes more harm than good. There is also a secondary story that explores the origin of the Arkham family and the asylum. In it we get things that mirror, or at least foreshadow, the primary story. For example Arkham’s mother being haunted by a bat in the same way Batman is (figuratively) haunted by his parents deaths, and the asylum is (metaphorically) haunted by Batman.
Watchmen (1986-1987) is an original comic book series by writer Alan Moore and artist Dave Gibbons. It is a story that examines many topics including: the superhero genre by deconstruction; the threat of nuclear war; how a being with superpowers would affect historical events. The primary story is that of an apparent murder mystery centering on a group of costumed heroes, and the one being with superpowers. Yet, this story gives way to a grander story by including added narrative plot lines from other topics, such as the three mentioned before. Watchmen also has a secondary story which mirrors, or foreshadows areas of the main narrative in the form of a supernatural pirate comic book tale a supporting character reads. There are also psychological examinations (via the narrative) of the superhero characters. For example how Daniel Dreiberg, alias the second Nite Owl, finds sexual confidence from costumed adventuring (Watchmen #7 ).
As one can see both titles use mirroring, deconstruction, superheroes, stories within stories, and psychology. Thus to consider them as totally dissimilar due to the vastly different art styles, and one having more well-known characters, is just nonsense.