My wife and I have been on both the Adventure of the Seas and the Explorer of the Seas. We found that they were almost identical, so we loved them both equally! They are very big ships. The Adventure is a little bit bigger, and is second in the world in size to only the Queen Elizabeth II. They both have great bars, spas, food and entertainment.
Just like Roland says, it doesn't matter but for fun........The Explorer weighs the most because of the marine science lab that is onboard. The Mariner and Navigator are technically the largest because all the cabin decks above the lifeboats were extended out about 3 or 4 more feet.
The best ship would happen to be the one I would be currently cruising on. Not that I have been on many, but I don't care which ship it is if I'm able to worry about nothing and have nothing that I am required to do!