I am a 'day before' person, but I have had a couple exceptions in the past few cruises where I had no choice but to fly down on embarkation day. In both cases I made it to the ship fine, but not without some worries. The last instance saw me sitting on the tarmac at my home airport on the morning of the cruise (Oasis pre-inaugural), because the FAA flight plan computer crashed and we were not approved to take off. It took about a half hour to resolve, which put me at a dead run through Atlanta to make my flight to FLL. I was the last passenger to board, only because that flight was a few minutes behind. Otherwise I would have likely missed the cruise. It's just about impossible to find an open seat to Florida on the day of the flight these days.
Too many things can happen to screw up a flight schedule. Just yesterday TSA had issues at more than one major airport which required them to close terminals and rescreen passengers.
I like not having to get up early to make a 6 or 7 am flight. Going down a day early gives you more choices, so we can take a later flight and not have to get up before dawn. Check in to the hotel and relax, have dinner, wake up refreshed, and grab the shuttle or a cab to the pier. That is the preferred method for us.