Display flexibility: I can pick a rendering that works best for what I want (e.g. optimized for high contrast or print, prioritizing/de-prioritizing specific types of paths, or public transport). If you consider derived maps, there is even more choice, e.g. I can get a topographic map based on it.
Usefulness while on foot. In well-mapped areas, OpenStreetMap has every little footpath between buildings, through parks and forests, ..., with information if it is publicly accessible or not. Google Maps is missing tons of them.
Offline functionality. (Google could change this, but I somehow don't see them allowing to download entire countries at once)
Another: dynamic updates - in case of emergencies and disasters OSM data has often been updated by volunteers faster than other sources to reflect the on ground situation. For current examples See:
Usefulness while on foot. In well-mapped areas, OpenStreetMap has every little footpath between buildings, through parks and forests, ..., with information if it is publicly accessible or not. Google Maps is missing tons of them.
Offline functionality. (Google could change this, but I somehow don't see them allowing to download entire countries at once)