I have not booked a cruise while on board. I would use my TA for this.
However, Princess has a future cruise deposit program that is only available while onboard. Basically, you can make a $100. deposit toward a future cruise. In fact, you can get others (friends, family) in on it too, and it includes an onboard credit when you finally make a booking. All this, as long as you do it while onboard.
For us, in our recent trip to Alaska, it allowed us to hold our $4400. cruisetour ($2200. ea) with just a $100. deposit up until final payment time.
While onboard, we again made the $100/person deposit against a future cruise. Princess will honor this for a period of four years.
I should add....you can, in fact, actually book a future cruise while onboard Princess, if you like. And No...there are no special prices onboard that cannot be matched by your favorite TA.
I have booked a future cruise aboard RCI ships, and got the lower deposit, onboard credit and a fair price. I did book that cruise several months in advance, and did transfer the booking to my favorite agent when I returned to land. During the months between the time I booked and the cruise sailed, the price dropped, and my agent was able to get thet reduced price for me. It worked out to be the best of all worlds. I got a reduced deposit, I got a nice onboard credit, I was able to transfer the booking to my favorite agent, and therefor got the great service I'm accustomed to, and I got the reduction in price.