Yes, the Liberty is a larger ship. The Triumph and its sister ship Victory have less buffet lines which can make going to the buffet a bit of a long line nightmare.
If I had a choice I would go with the Liberty assuming everything else is equal (ports and cost) But the differences in the ships are not so great as to offset a major difference in cost or itinerary.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007