I think either one would be a good month, possibly a bit warmer in March. Late Feb is always decent and its before all the spring breaks start. If you do go in March, you'll notice higher prices, due to more traveling for spring break.
not much variation in the weather during these two months, you will pay higher rates these two months because February is winter break time for a lot of primary schools(around President's Day) and March is Spring Break time for the college crowd.
What we are looking at is an Eastern Caribbean prolly on Celebritys' Millinneum and it does look like late Feb. is a little cheaper than early March. Not really sure if there will be a lot of young uns on Celebrity anyway but if everything else is equal weather wise we will prolly go with the cheaper fare in late Feb.
I've been on 3 cruises in March. The weather has always been warm with little rain. The only exception was this past March. We did experience some high winds and rough seas on one night. The boat pitched and rocked enough that they cancelled the evening's shows. The boat was also full of spring breakers from Ole Miss. I can't say enough about how well behaved those young adults were on that trip. They were definitely having a great time but they were polite and mannerly. I loved watching them arrive for dinner each evening as they were more appropriately dressed than many of the more mature adults.