This was our first cruise, so no comparison with other cruise lines.
We had an inauspicious start: it took, Friday lunch time, two hours to drive last 20 miles to Port. Main cause of delay was road works at entrance to Port - don't know if ABP or Council, but minor works with two men with "stop / go" signs at Port gate next to traffic lights - the lights went green, men showed "stop", lights went red, then, obviously, "go". We had planned lunch in Southampton, so had plenty of time, others did not. The departure of Azura had to be delayed.
We had booked car parking, and despite VERY surly staff (who had probably suffered 100's of people complaining about traffic delays), the service was really efficient - luggage moved by staff to conveyor within seconds of parking. You then enter terminal and within twenty minutes were on board.