A full cruise in no way compares to a crowded Magic Kingdom. You will experience lines to see characters and get pictures taken. Other than that, there is lots of room on the ship.
I've been on one totally full ship. Most of the time, when they say it is "full", there are still rooms available. For instance, the 2/7 Magic was listed as "full," but as of 2 days before, you could still book the trip in 6 different categories. In addition, a large section of the 7th deck was closed for renovations (starboard aft area, including the laundry room). Even with the ship totally full, there is plenty of room for all.