Both of them are autobiographical accounts of their authors' (both of whom being female) experiences with subjects related to the LGBT community with a comedic edge. In Hanayome's case, it deals with the author being a transwoman and Sabishisugite deals with the author's experience of being a lesbian.
Both are manga that deal with themes of depression, yet go off on their different ways as interesting character-driven stories. You are not guaranteed to have a good time reading through either of these, but it's a very accurate depiction of what depression does to a person. Worth your time.
Both talk about self-knowledge, sexuality and other emotions with deep psychological aspect. Is interesting see the different visions of the world that make different the two series. Inside Mari is more tense and heavier than Sabishisugite, but even so a great manga.
Both of this series deal with lgbt issues in a different, more mature and relatable way, which lgbt people themselves can feel identified with.
The main difference is that Shimanami tasogare has a much more dramatic atmosphere; whereas My lesbian experince with loneliness is more comedic, which, in my opinion, is for relief, since it deals with very sensitive and heavy topics, and it is an autobiography. Of course, this doesn't mean it shouldn't be taken seriously.