Don't forget to throw SECURITY into that mix. Remember that if your Disney excursion is late returning, they'll hold the boat for you. If you make your own plans and return late . . . well, you're out of luck.
Having said that, I would make my own plans IF the situation was right:
I'd have to know that I was either saving a good bit of money OR that I was getting something that Disney couldn't offer -- I wouldn't "go it on my own" to save $5 per person.
I'd have to know that my transportation back to the boat was very sure. I would not, for example, try to do the Myan ruins tour (I forget the name) that requires a tender AND another ferry to another island. There are just too many little things that could hold you up. However, I would gladly do an on-your-own excursion that only required a taxi ride.
I'd make sure I had a cell phone and the phone number for customer service so I could call if I encountered any problems. I'd be ultra-double-sure of the back-on-the-boat time.