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I have just cruised on QE2 for the 1st time. I was in Mauretania class. In my opinion - the food in the restaurant was poor as was the service, the cabin on Deck 5 was adequate but the noise of the engines very loud preven ting proper sleep, the corridor and ambience shabby/tatty. Entertainment mediocre, very limited activities (apart from the frivolous) etc. My 13th cruise and very disappointed compared with QM2, Constellation, Oriana etc. I think you might go nuts on a world cruise. Sorry to be such a moaner but think you sholuld look to another ship. The QE2 is old and they obviously don't spend money on Mauretania class.
QE2 is an old ship, I would book a two week cruise on a nice modern ship first to see if you like it, perhaps P&O's Oriana, Celebrity Millenium, or Sea and Sun Princesses would suit, all nice ships.
Go for it and have a nice time.