There is quite a bit of difference bewteen the Liberty of the seas and the Serenade of the the Seas.
The Serenade of the Seas is a Radiance Class ship it doesn't have a Flowrider, an ice rink, or a Royal Promenade. It is an older ship its Maiden Voyage was August 1, 2003. Length: 962' and Passenger Capacity: 2,501.
The Liberty of the seas is a freedom class ship has the Flowrider, ice rink (with ice shows) and a Royal Promenade where they have a parade. The Liberty of the seas Maiden Voyage was May 19, 2007. Length: 1,112' and Passenger Capacity: 3,634.
I like new big ships so I would go with the Liberty of the Seas. I have not been to the ports of call on either ship so I can only speak to the differences in the ships. I normally cruise out of California so I know Alaska and the Mexican Riveria. I do know Grand Cayman has Stringray city.