Hi Laura,
Having been on Explorer and Golden Princess, I'd have to recommend Adventures of the Seas, only because you mentioned that you would be cruising with your 4 year old daughter. While both cruiselines have great kids facilities, I think there is just a lot more thats offered on these "Voyager" class ships for families/kids. There is virtually something for everyone, no matter what age.
In fact our Explorer cruise is so far the favorite for both my husband and myself, can't wait to try another one, but first we're doing Radiance and seeing what kind of ship this class is. I love Princess for their food and service, and also the fresh water in the pools, very nice!
Whatever cruise you do decide on, have a wonderful time and let us know what you do finally decide.