Twin ideas:

Lilith is generally the more reserved and elegant one, partially out of a need to live up to a self-imposed concept of what a well-bred vampiress should be, and partially as a result of having to hold Carmilla back when she gets a bit too… Carmilla. She is patient, long-suffering, and used to going along with what the strongest personality in the room wants, but if she does reach a point where she thinks that rebellion or vengeance is necessary or useful, she can come up with creative and concise plans toward that end. She tends to see Carmilla as slightly more impulsive and self-centered than she actually is, and when they switch places, tends to play Carmilla as being a few shades shy of thoughtless and a bit more entitled. Her personal tics and “tells” include biting her lip when she’s considering lying, placing her hands behind her back or clasped at her waist to enforce her posture while standing still, and her glances toward people other than the one she’s talking to.

Carmilla is generally the more hot-tempered and party/sporty one. She’s used to having to pull her sister along when Lilith gets caught up in studies or is hesitant to quickly come to a solid conclusion or active decision. She likes to dive into things feet-first, not entirely without looking where she’s going to land but prepared to improvise as she goes. Her schemes generally have more variables than Lilith’s, which she adjusts to as she thinks of them. She’s not self-important, but will not take rejection or criticism sitting down when she believes that she has rightfully earned something. She is stubborn, and once she decides to do something, there is no stopping her -- including herself (she took those singing lessons for a reason). She sees Lilith as slightly more withdrawn and status-concerned than she actually is, and when they switch places, tends to play Lilith as a few shades shy of compulsively orderly and a hair more stand-offish. Her personal tics and “tells” include making direct eye-contact just a little bit more than normal, occasionally running a hand through her hair as if to make sure it hasn’t fallen out of place, and rocking back from her toes to her heels when she wants to change subjects.