As the town busybody, Miss Stephanie makes it her business to spread gossip, the meaner the better. She's the Finch kids' main source of rumors about Boo Radley, and takes as much delight in the ghoulish details as Jem does.
Occasionally she tries to hide her unladylike curiosity, like when she pretends that she's going into town for any other reason than to watch the Robinson trial, but most of the time she doesn't do much to disguise the fact that she knows more up-to-the-minute dirt than Facebook. (Ugh, can you even imagine what her status updates would look like?)
Miss Stephanie doesn't change much if at all over the course of the novel, but Scout does: she learns not to let those snarky comments get to her, showing that she's a little bit closer to growing up into a lady.