They are quite different, because Miami is on the east coast and Los Angeles is on the west coast. Because the Earth rotates in the direction it does, the east and west coast climates are influenced in different ways by the land and ocean. Both places stay above freezing year round and snow is a rare thing in either metropolitan area, although there are tall mountains around Los Angeles so snow falls on those every winter--there are even ski resorts. It rains about 4 times as much in Miami as it does in Los Angeles. In Miami the rainfall is concentrated in the warm season, while in LA it is in the cool season. It is generally more humid in Miami, because the ocean is about 12-15 degree Fahrenheit warmer. In the fall Los Angeles can have strong hot, dry winds from Santa Anas, while Miami is subject to tropical storms and hurricanes.
IRRELEVANT ASIDE (like Horse's answer): I took a look at how "freedom" is ranked in the survey that Horse talked about. Apparently if a state lets you have an assault weapon and a silencer for your gun they're ranked higher for freedom, but they don't even consider whether young people can get birth control or whether women had access to abortion, but they do credit states if they allow cousins to marry or if they let you smoke in restaurants.