Strollers are a godsend and hell in Asia. I've lived here for the past 4 years and my kids (currently 2 and 5) are usually in the stroller when we travel. I have a Graco Sit and Stand so the older one is in the back. It's still quite big, bigger than a single, but smaller than a typical double, so it is more like a 1.5 Handles pretty well, and is a god send in the airports. However, most Asian roads and even many places such as shops do not handle strollers well, especially a 1.5, because they are small and cramped. Many sidewalks are treated as extensions of places of business, so you will be forced onto the street. This makes a stroller both a hassle and a blessing because while it is inconvenient to navigate around all of these obstacles, keeping them in the stroller often keeps them far safer than letting them run around (and possibly into traffic).
The kids usually sit in the stroller on the subway. Many places are difficult due to a lack of elevators or even escalators. I think bringing a stroller will ultimately depend on how well you can handle your children in hectic and possibly dangerous environments. My little one is too small to understand well enough so its worth the extra hassle to ensure her safety. However, at 4 years old it will depend a lot more on the child. If he tends to be more rambunctious then I would probably bring an ultralight umbrella stroller just in case.