I've recently done a transatlantic crossing on the Queen Mary 2 utilizing their kennels for an extended working trip abroad for the summer (to be truthful to get out of the Florida heat). The crossing between NYC and Southampton went smoothly once onboard. The Kennel Master Oliver, and his assistant John are fantastic with the dogs and there are multiple hours to visit - 8am-12pm, 3pm-6pm and a run around the deck when other passengers onboard who miss their pups at home can interact.
The dogs while anxious at first and for a bit during the voyage, surprisingly created a nice pack. There were those of us who were there for the entire time for visits, and those who came and went. The easiest crossing were for those traveling as families or couples who would take shifts hanging out with their dogs, so the other could enjoy this fantastic ocean liner. As a single passenger, in hindsight, I would have asked a friend to come along with so I could get some sleep, go to a show, even get some work done, etc.
I was the only person traveling who was making a round-trip, and most others were moving to the UK. What was interesting versus flying is that the clocks slowly move ahead one hour for five of the seven-day trip, eliminating for the most part jet lag upon arrival. And while the crossing was a bit stressful at first, the dogs and owners got into a routine, and the seas of the North Atlantic were calm. Since all the paperwork and vet information was done prior to boarding, we disembarked with no need to stop at immigration/customs or animal control.
That leads to the stress of getting all of the paperwork done which includes sending to the USDA and vet visits plus tapeworm treatment (required by UK), done within a 10-day period including weekends. It being July 4th weekend, that left little time, and because I was traveling from Florida added more stress to the mix about timing. That stress was shared by most, unless people were originating in NYC. My dog doesn't take very long drives with hotel stops well, so by the time we got to NYC we were a stressful mess but luckily all paperwork completed correctly, and once boarded, it was easy with the help of Oliver and John. Oliver has been doing this for 15 years, and is truly a dog whisperer.
Final thought, is this is a great option for those who do not want to put their dog in airplane cargo hold. Only caution, be prepared for the multiple things to prepare and the stress which comes along with it. The Kennels Team at Cunard is helpful, offering a lot of preliminary information, but a lot relies on the individual passenger and their vet. I can see why the kennels were filled with most people returning home versus myself doing a round-trip, although I'm told the way back to the USA is much easier, with only an upload of rabies certificate into the CDC website. I'll be sure to let you know how that goes upon my return.