Unless you’re going very slow (walking speed) — stick to the street.
BTW, around here it’s illegal to ride on sidewalks, or across crosswalks. If that’s the case where you ride, you could be asking for some hefty fines.
http://www.kenkifer.com/bikepages/health/risks.htm (scroll down)
Riding on the sidewalks in urban areas , it is a given that one doesn't try to go > 1.5x mean pedestrian speed. Besides, collisions with pedestrians are not lethal to bikers.