Even though booking tours through the ship are more expensive I feel more comfortable doing it that way. One big reason, if your tour gets late getting back to the ship the ship will not wait for you if you book the tour privately. On the other hand if you booked through the ship and your tour is running late the ship will wait for you. Also, better chance of getting your money back if the tour is cancelled. I don't go on a cruise for more stress worrying if we will get back to the ship on time. We have done Princess tours and have been happy with them. We are booked again for this December on another Princess ship and have our tours booked with them.
The decision is what you feel comfortable with doing.