We have not sailed on the Destiny, but we have sailed out of San Juan. I believe the uncomfortable complaints are coming more from the fact that it will probably be the most "international" cruise you will ever be on.
We had a wonderful time. But it was definately a different feel. Little things like our tablemates not speaking English was odd.
Each cruise is different, but I believe the main complaint is that if the ship does not fill up, Carnival deeply discounts the cabins to locals who may (or may not) have the same culture we are used to. That is where the complaints of rude, over the top loud, aggressive behavior has come from. How much of that is accurate and how much is just because it may be a different culture than folks are used to is hard to pin point. I was raised around Cajuns, so these folks were tame in comparison.
I would suggest that if you want to sail on the Destiny that you do it when San Juan schools are in session.