These are both works by Sakuraba Coharu, and they share a similar sense of humor. Both series revolve around school age children and their comedic interactions, but they are intended for an older audience. Sakuraba gets a lot of laughs out of a class of fifth graders on the cusp of puberty in Go no Ni, but the wider age range of characters in Minami-ke and the great dynamic between the three Minami sisters allows for even more variety of hilarious situations. If you enjoy one of these manga, you'll almost certainly enjoy the other.
both 4komas and light hearted humors. Lucky star isn't about sisters or anything and minami isn't about purely high school girls but they're pretty similar. you can relax to both of them before sleep or during meals or something.