I've sailed five times on Disney so I was nervous about my first Royal Caribbean experience. It was my friend and I, both in our early 30s.
With the port being much larger than Port Canaveral, it was also more chaotic but the taxi got us there and out without problem. It seemed a little disorderly but we found someone to take our luggage and got into the extensive line for security, which moved very quickly. I can't believe the number of people that were carrying luggage on with them. I didn't even know this was an option. The terminal was definitely very basic, but it did the job and we were checked-in and ready to board without much fanfare.
Compared to Disney, here are my areas of comparison:
Pool areas - more extensive than Disney but definitely not heated
Dining - Windjammer quality was very low but main dining room sand MyTime dining was awesome
Aesthetics - Disney wins on this one, better overalls ship upkeep and decor
Spa - Disney also wins but I won a free treatment so I can't be too hard on it
Activities - Both offered extensive activities
Shows - Surprisingly Liberty wins this one due to the variety...Saturday Night Fever was spectacular
Stateroom - Disney wins for quality and decor
Service - Disney wins by far, not one staff member greeted us in passing in public areas
Cleanliness - Disney wins and Johnny Rockets was disgusting
Gym - Huge and extensive
It's a tough comparison overall. If money was no object, I would sail Disney again. However, Liberty's prices are about 1/2 of Disney so the value award would go to Liberty.