We are on this cruise, first time on Princess. We were advised by another traveler who lives in the UK that the National Express was a good choice. It was quite inexpensive and we paid an extra $5 each to be able to take a later coach should our plane be delayed. We are arriving a couple of days in advance, so the Princess transfer was not an option, but it seems the National Express is cheaper than their transfer.
If you book a train, be sure to check the schedule and transfers. We will be taking the train from Southampton to Paris after the cruise and our TA has advised we will need to make 2-3 transfers between Southampton and London and then a straight shot from London to Paris.