Check as many reviews and forums online as possible that discuss both ships. While these are just opinions from normal customers, reading enough of them with an open mind can give you an idea of what the lines do best. Check the date of any posts in forums. In 2011, some of the forums dated back to 2004. Look for forums and reviews from the past year for the most accurate opinions.
Read the reviews for the ship issues most important to you. If cabin size matters to you, do a search on ship reviews and cabin size. Some other elements reviewers tend to point out are the professionalism of the crew, the availability and range of food, the length of lines and kid's facilities.
Find and compare the entertainment and shore excursion opportunities on both lines. Be wary of islands owned by the cruise line, like Royal Caribbean's Coco Cay. The island is fine, but beach can get crowded and the whole thing comes off as a tourist trap.
Consider the crowd. Carnival tends to draw a younger crowd than Royal Caribbean. If you prefer not to be around kids, go with Royal Caribbean.
