Both these cruise lines are owned by the the same company carnival plc an American company ? same company different marketing.
I would certainly take a USA departure port over a UK departure port. To put it diplomatically the Americans seem to know how to behave: when it comes to tips, dress and not pressing every button on the elevator etc etc when cruising which is sadly lacking amongst certain UK travelers. Just MHO.
Short distance P&o is fine, Long distance Princess. Flights with P&O are normally on a Thomas Cook (cattle market), Princess are scheduled flights and you are normally put in hotel before flying hom.
The difference between the two companies is, P&O is aimed at the British market and Princess the American Market. Also, Princess has a much younger average age group. P&O's new Ventura is finally taking them into the 21st century and should attract a much younger market. Saying that, I have enjoyed the 6 P&O cruises I've done in the past. No one can say what's best for you, you need to try a few shipping lines yourself because we all like different things. I love Royal Caribbean but fellow cruisers I've met hate the product. My answer to you is yes, I would book Princess over P&O purely on the basis that the Americans like to have a good time and unfortunately, on some of my P&O cruises, I've shared tables with some very miserable people who just like to moan!
We cruised with Costa cruise line, on the Costa Victoria which is an european cruise line catering for the many nationalities in europe. On our cruise in the summer the majority were italians with french, german, and scandinavian to name but a few other nationalities, the english and americans were in the minority. We thoroughly enjoyed the cruise experience but would prefer to go with an english/american cruise line next time, purely for the language barrier [on our part i might add] plus the italians prefer to barge their way through everywhere and have not got a clue about manners. Hope this helps in some small way.