@Ez-8 Ok, let's go by points.
First, welcome in the wonderful world of yuri <3. If you haven't read Hanjuku Joshi, you really should read it.
Yes, Yae and Chitose relationship is more mature, also because it is more physical: they have sex, like, in the second chapter, and many time after that; Kase and Yamada only had sex once, towards the end, and the scenes are not very explicit (if I remember correctly). Hanjuku Joshi is much more explicit and more realistic in some ways (with the gender identity questions you mentioned), Kase-san is a flaffy romance comedy, not too deep or realistic.
Yae insecurities are more deep and serious, Yamada is mostly an airhead; Chitose and Kase are similar, but tomboys like them are an archetype of yuri, you can find similar character in other mangas.
Kase and Yamada fall in love with each other before (independently) becoming friends, and both are well aware of their feelings (well, Yamada has some doubts), then they confess and start to date (a typical yuri developement); Yae and Chitose start as mere acquaintances, become friends, and only then do they begin to develop romantic feelings, which grow and strengthen over time (where the relationship between Kase and Yamada has a lesser evolution).
The presence of another couple is not such a big issue, but is relevant that they play a fundamental role in the development of Yae/Chitose's relationship (they give them many help and advice); Kase/Yamada don't confront with other lesbians, so they are alone in dealing with problems and issues of a relationship (and so they are constantly clumsy and insecure).
IMO, the two manga are almost completely different, except for the physical appearance of the protagonists (but with swapped boobs XD). In some ways, Kase-san is more similar to Girl Friends (p.s. if you haven't read it, you MUST do it).
