Not found this to be the case so far, only benefit is you have more cnahce of getting on the trips you want to go on. If one you booked was cancelled say due to lack of interest you will get a refund on your seapass account. Some prefer to do their own thing and hire a taxi/minibus at the port and this can be cheaper but best if you know what you are doing or meet up with some like minded people on the ship who have done this before and you can share with them. If there was a day when you had booked a excursion on-line and wanted to go with a small group to do your own thing if you advise early enough you should be able to get a refund. Hope these thoughts give you some help and enjoy your cruise in the Caribbean a lovely place to be.
The price of the trips on P&O is the same whether you book on line or on board ship. The advantage of booking on line is where space is limited you can get a guaranteed place. Where the trip involves a coach tour they just seem to add more coaches to suit the numbers so it does not seem to matter. There is usually a cut off time of 48hrs before the trip .