Yes, there is a big difference between Celebrity and Carnival or Princess. Probably the most telling thing is that there are many truly luxury touches on Celebrity as well as amenities, food choices, service levels, etc. that put it well above them, in my opinion.
That said, each cruise line has its own niche, so think about what it is you like and what you might like to be a bit better or difference and then engage in the conversation. For example, the fact that Celebrity has an elegant piano bar (Michael's Club) or a truly wonderful formal restaurant (Murano) may be irrelevant to you or, in fact, an infringement on the casual experience you desire.
OK, now here is the next installment of my blog: This Is My Yacht - Luxury Cruising and Travel: Goldring Travel's 2011 Celebrity Century Cruise - How Close to Luxury Can Celebrity's Smallest Ship Get? Part III