I took a double stroller with me in 2000 and I was glad to have it. If you rent, then you won't have one to use at the airport or in the resorts. Also, I frankly don't like the idea of my kids sitting in a stroller that thousands of other kids have been in and who knows when they were last cleaned. Finally, the cost of renting a double or two individual strollers over several days really adds up to the cost of a brand new stroller in the end.
That's my .02 anyway. I will have 3 under the age of 8 when we go in November and I'm trying to decide if I want to bring just the double, or a double and a single. If one has to walk and the other 2 get to ride, it will probably not be very pretty...
Have a great trip!