I'm going to buck the trend and say that with a 1 year old, I would go with the cruise, hands down. The access to child care is so great! It's a much more relaxing trip without most of the running around. Yes, the dinners can be long (if you take early seating, they are generally shorter than the more lingering late seating) and we have always been lucky that our child is easily distracted by lots of people being around, so long dinners aren't such a hardship for us. You know your kid best.
We also liked that when one of us had to be in the room for daytime naps or early bed time, the other one could go out and do/see stuff and not be really far away from the room. Once you're in for the night at a Disney resort, you're in for the night, but on the cruise ship, my hubby could watch our daughter for a while while I went and took in a movie or watched a comedy show and then we'd switch off. With daytime naps, one of us would take a nap with her while the other one (usually hubby who doesn't nap) would go do something fun or just relax out on the deck.
Being able to have child care while we went off the ship was also super awesome. Yes, it's an added cost (and it does add up fast) but it was great to be able to go on the kayak/hike/snorkel excursion and know that our daughter was being well taken care of and enjoying herself.