March can be a little more expensive due to spring break. The spring break crowds aren't the best to cruise with anyway.
I have been on a number of Carnival 7-day cruises and they have all been very good and relaxing. The key is to avoid short cruises and to avoid the crowded times if possible; especially avoid spring breaks. This goes for all cruise lines.
There are plenty of places to get away from crowds even if the ship has a high number of guests. Crowded periods are not a deal breaker for me but I can be flexible with my dates when not traveling with kids in school.