We took a transatlantic crossing from Southampton to New York. We travelled in a P1 suite on the port side (specifically booked so we would see the Statue of Liberty from our balcony).
The ship is lovely. It's classic ocean liner and if you're looking for this kind of experience then this is the ship for you. The transatlantic crowd is quite cosmopolitan and certainly dresses for the occasion. The formal nights are quite a sight and you will see many spectacular dresses.
If space and luxury are what you're after then you will enjoy a Princess Grill suite. It has a walk in wardrobe and feels extremely spacious with lots of storage space. On long cruises I would feel very comfortable in a cabin of this size - it's very generous and well appointed. Fresh fruit is changed daily and the bed was very comfortable. We slept very well.
Excellent suite. In the middle of the ship so you don't feel very much movement. Perfect for westbound transatlantics as you can see the Statue of Liberty from your balcony.