Our first trip our sons were 9 and the younger had just turned 6 the previous month. They both did fantastic without a stroller and never had a problem on an eight day trip . The only thing was they were star struck taking it all in so we had to walk slow and keep a close eye on them or hold their hands. My wife wanted to take a stroller for the 6YO but I insisted I would carry him if he got too tired. I did two times, after fireworks and when he fell asleep on the bus. After the trip my wife was so happy we did no take a stroller seeing people fight with them in crowds, getting on the bus and at the backups at stroller parking. There are clear advantages to having a stroller though.
If you were to take one I would lean towards a single and let them swap. Having watched it looked significantly more difficult to maneuver a double than a single when busy.