Now I'll try to choose my words carefully. Previously, I was set up in a previous thread sometime back in reference to the "great stroller debate" and slapped on the wrist for something that was considered "a minor personal attack". I feel that those ages are approaching the age that is too old for strollers. This is based on our personal experiences with "Kamikaze" stroller pushers who use them as battering rams to make their way through crowds! Nine times out of ten, the stroller was occupied by children that could have well walked, or even unoccupied. Yes, children get tired, but they are in the best place in the world, and should be disciplined enough to act accordingly. Midday breaks are highly recommended, and are best taken advantage of back at resorts. I have no problem with strollers, per say, but rather how inconsiderate many people are when using them unnecessarily! And before anyone tries to say otherwise, we have been going since my daughter was very young, and have never used a stroller. Anyway, my $0.02.
It is not always a matter of "suck it up." We have gone in June/July. It is HOT. Even a kid who is in great shape is at a MUCH greater risk for dehydration and heat exhaustion than an adult.
We took a small one when my son had just turned 5. I also liked being able to have a soft sided cooler with cold drinks in the heat. But we mainly used it for storage and long treks (think needing to get from Future World to an ADR in France or from one end of AK to another). Of course, it is best to avoid crossing the park, but with FP+ and ADRs, sometimes that gets difficult.
For those ages, I would probably bring a small something with storage and a canopy. Definitely not a double or sit and stand. They kids can take turns.