"Stature" can mean the same thing as "height", but it's formal, probably too formal for most circumstances. It's more often used as a synonym for "importance" or "reputation". "He is a man of great stature - he's won two Nobel Prizes". When used to refer to people, it's probably most used as the adjective "statuesque", which combines the senses of "tall" and "dignified". I've only ever heard of a "statuesque woman", not a man. "Height" can be used for anything, not just a person. You can talk about "the height of a building", for example. It would be weird to talk of the "stature of a building". "Height" also has a secondary meaning of "most intense" ("the height of passion") or "most outrageous example" ("the height of rudeness").