I agree with diveborg that it partly depends on how long your ship will be in port. I did the Belize dive excursion from a Carnival Cruise. The dive shop's boat picked us up and deliver us back directly onto the cruise ship. The divers were the first group allowed off the cruise ship and we were almost the last to return.
I believe all those booked on ship-sponsored excursions were tendered off first, and those who had not booked an excursion had to wait until last and take a number before they could get a tender to the island. So, if you are making your own arrangements, you may want to check with Princess to see if have this procedure as well. If so, it could affect your scheduling by as much as 1-2 hours, maybe more.
Knowing what I know now, if I had it to do over, I'd probably stick with the ship's excursion again. Though it was overpriced, the timeframe (at least with Carnival) was so tight that any unforeseen circumstances with a personal arrangement easily could have meant missing the boat... literally.