We have recently cruised with both Royal Caribbean and Celebrity. Both ships carried well over 2500 passengers. Years ago we cruised the Eastern Mediterranean on a Greek ship which only held under 300 passengers and have also done a couple of river cruises.
The difference is very apparent. The larger ships provide indifferent service and basic restaurant food whilst smaller ships provide excellent food and knowledgeable staff. We will never use RC or Celebrity again.
Our cruise with Celebrity Solstice in October 2012 was not a good on board experience. The stateroom was large and well laid out but the service in the restaurants was appalling. Whilst there was a reasonable selection on the menu, the food was always served on cold plates and we never had a hot meal. The service was so slow on occasions that we were too late for the shows and the Captain's Welcome Toast. Our meal time was 8:30pm and on the Captain's Welcome evening we didn't finish the meal till after 11:00pm so couldn't attend. When we didn't immediately leave after finishing the staff were extremely rude and made obvious moves to make us feel uncomfortable. We also bought a drinks package and were horrified that the assistant waiter kept pouring our bottle of wine into the glasses of the other passengers we were seated with. One evening we objected to this more than once but he still continued to do so.
The other annoying feature was that we were constantly bombarded with staff attempting to sell products: photos; restaurants requiring extra payments; drinks packages; special offers in the shops; etc. etc. It seemed that Celebrity were only interested in fleecing us of as much money as they could.
Overall we enjoyed our cruise simply because we visited such lovely locations. The embarkations and disembarkations were well organised for such a large number of passengers. It was just such a shame that the experience aboard left a lot to be desired.