I am a fan of both of these shows, but I just finished watching the second—and apparently last—season of Enlightened and couldn't help but notice some similarities between the two.
~~ Both shows portray tall long-haired white women in their early 40's beginning a career renaissance of sorts.
~~ Both woman are portrayed as being the underdog who was once on top and is trying to recapture some former glory and create new heights in their careers.
~~ Both women are narcissists who think the world revolves around them. Enlightened's Amy is certain that she is destined for greatness. The Comeback's Valerie is certain that the spotlight is always concerned, or should be, only with her because she had once been the star of a popular television show decades earlier.
~~ Their utter lack of awareness as to how they come off to others, which is very badly pretty much all of the time, consumes much of the show. They both suffer from social awkwardness that manifests itself in similar ways, such as the forced smile they employ even when the situation should call for weeping or in the careful and studied way they express themselves during moments that should feel spontaneous.
~~ The humor of both shows lies in how uncomfortable scenes are to watch. They both have a high cringe factor, especially because both women tend to approach people who do not want anything to do with them. With Amy it's Krista, her former assistant, who she constantly saddles with inappropriate favors or other expressions of friendship that are clearly—to the viewer, anyway—unwanted. With Valerie it's Pauly G, one of the writers of her new show who has done everything to communicate that he loathes her. Yet they both keep coming back to these people for more and the tension continues to escalate as we watch between the fingers covering our eyes. It's an intense neediness in both characters that is unmatched by even the strayest of puppies, and yet it's also a longing by both of them that is familiar to anyone who has ever yearned for their own personal best.
~~ Both women have a tendency to just stand up and give inappropriate speeches that make a situation that is not about them at all reoriented around them. Valerie does this repeatedly at table readings. Amy does this often, most notably at Krista's baby shower.
~~ A smaller thing, but both shows use the term "put a pin in it" repeatedly.
~~ Both shows feature this actress, Bayne Gibby. She's a minor character in both, yet is one who appears in many scenes, even if she says nothing at all. (Usually in The Comeback, her incessant eating of various things is used as a site gag.)
~~ Both were critically acclaimed HBO shows and both were cancelled due to low ratings. People could not handle the cringe factor, apparently.
I'm sure there's more. Please feel free to add anything.