IF you are a worrier, stick with the
DCL excursions because the worry ain't worth the money!!
And the money you will save is not really that much, for example at grand cayman the difference in the DCL and cptn Marvins excursion to sting ray city is only about $5 per person (ie $20 for a family of 4 - on top of the $4,000 + that taking the cruise costs - therefor not a big savings).
There are advantages to the independent operators however. Usually you can work on your schedule, not DCL's. You also may be doing more that what a similiar dcl excursion would do (ie cptn marvins may have more stops than dcl).
And there may be some things that you would like to do that DCL does not offer - in that case you would have to do them on your own.
YOU DO NOT WANT TO MISS THE SHIP WHEN IT PULLS OUT OF PORT!!! If you are not on the ship be sure to have a camera, because you will get a picture no one else has, that of the ship leaving port without you.
If you do your own excursion or day at the beach, just make sure you give yourself enough time to get back on board before boarding time - because the ships have left people behind. Along those lines, make sure that you change your watch as the ships time changes (it changes with the time zone it's in). That seems to be a "big" problem on St. Thomas, people forgot to change their watch and end up missing the ship because that thought that they had pleanty of time.