To correct a mis-statement, Crystal, Oceania and Silverseas are not ranked as "premium" cruise lines but rather "luxury" cruise lines. While Princess, Holland America, Celebrity and several lines are ranked as "premium".
Having sailed on Princess, Holland America and Celebrity, I agree that the service is premium on all of these cruise lines. I never have experienced anything but premium service on any of the cruise lines that I have sailed, so that issue is a non-starter with me when comparing cruise ships. I really don't think there would be much of an improvement in the service area, even on the luxury ships such as Crystal. On the luxury ships you would find an improvement in accommodations and food.
For me, the service has never been an issue with the Millennium class ships but the recurring problems with the propulsion system on the Summit, Millennium and Infinity, is an issue when comparing the Millennium class ships to those of other cruise lines and even the other ships in the Celebrity fleet.