like the way each of them treats taiki - risai treating him with kid gloves and she's much like an older sister being massively overprotective of him while rousan calls him a monster constantly (even when he was a child) and is the only person around him who never underestimates him and his nature.

their respective relationship to gyousou is also very different. risai is the newest addition to his retinue but still serves with the utmost loyalty placing the emphasis on the fact that he's the emperor. rousan, on the other hand, is one of gyousou's oldest retainers (being there before kouryou- who was present at the tetsui incident) and while she does respect gyousou as a person, her scientific curiosity about providence rises above both that and loyalty for a ruler one feels.

then of course their relationships and views on heaven. risai at first is very conflicted by it, both resenting the fact that heaven abandoned tai and begging for it to save tai from its plight. later on this outlook does change considering that she got to experience the workings of it firsthand and her view takes on more of a "it's just works the way it does and there's nothing I can do about it" viewpoint. but rousan is endlessly fascinated by it to the point of trying to push things in the wrong direction just so she could see how heaven would right the course of tai's future.

another thing is the patriotism that risai exhibits for her kingdom and how everything she does is for the sake of tai and how that's deeply engrained ih her sense of purpose, while rousan as a koushu certainly holds no sentiments like that.