95-99% of the time, I think it's a better to ride on the roads. But I can't emphasize enough how stupid it is to dogmatically believe that 100% of the time, no matter what the specific scenario is, the road is better than the sidewalk. Smart living requires adjustments and improvisations, not slavish devotion to a set of rules, and smart cycling is no different.
Last night after my commute home, I went out with my car to do some shopping. The way back followed the same route as my commute... there's a area turning on to the last road that curves and is very narrow. There's room for one vehicle and not much else. It's also a steep climb. Rounding the curve I suddenly realized there was a cyclist ahead, slowly lugging up the climb. Being alert enough I slowed and waited for the road to widen enough for me to pass. By the time I saw the cyclist, I was already almost on top of him. When I'm commuting on the same stretch I take the sidewalk, every time. Over my entire 10.5 mile commute there's less than 1000 feet where I ride on sidewalks, including the stretch I just mentioned. If I insisted on taking the road during that stretch, it's almost a guarantee I'd be hit by a car eventually.