Clydebuilt, among the best cruise ships when it comes to seakeeping would probably be NCL's Star/Jewel class ships.
Rob, the purpose of having >TUG< or >NO TUG< on the side of the ship is to prevent the tug operator from pushing on the shell doors and tender platforms. If you look at the QM2, her tender platforms have >NO TUG< written on them. Some ships take this a step further by having saying >TUG<, >TUG AREA<, >TUG PUSH HERE< or the equivalent marked some distance away from the tender platform, the intended purpose being that the tug operator will not but his tug between the >NO TUG< marking and the >TUG<, but not all ships have this additional marking. The QE2 does not have a need for these markings, as she does not have any tender platforms.
And on your second point, lets forget about passenger ships for the time being and look at a container ship that crosses the North Atlantic on a frequent schedule, 12 months a year, year after year. Is that container ship built to a different standard than one that never goes into the Atlantic at all? No, it's not. It is expected that any ship, no matter where it operates, must be able to weather any storm it will come across. The Atlantic by no means has a monopoly on bad weather.