Just as many people will swoop in and tell me that I NEED a stroller for my 4.5 year old and I should run and buy a Mac, so it works both ways.
That being said, we are not bringing a stroller for him next month. We brought it in December and used it less than 1/2 the time. If he got tired during the day, we would sit on a bench for a short rest, cool off, grab an ice cream, then get back to business. It was nice not having to go search for it after the rides, fold it on the buses, and push it through post-parade crowds.
HOWEVER, it was my husband's idea to leave it in the room and I was hesitant so I told him that if DS got tired, he would be the one that had to carry him or walk across the park and pay for the stroller. He did have to carry him a few times at night going back to the buses, and of course he fell asleep on almost every single bus ride back to the resort, so then we had to carry him back to the room. But since I have a lightweight son, a construction worker husband and only 1 kid, it worked out fine. Your kids are older and there's 2 of them, so I don't think that would work for you.
Kids get tired and a stroller may come in handy, especially if you are planning loooong days in the parks and staying for fireworks etc, or if your trip is during the hot summer months. People will give you opinions both ways. You know your kids (and yourselves) best.