Absolutely, eg. the woods near my house have trails mapped out in OSM that don't exist on Google Maps.

I also find Google's colour scheme rather obnoxious when I want to use the map to actually orient myself (instead of it being merely a convenient geographical background for displaying POIs and route planning) – forests aren't displayed at all once you start zooming in and the distinction between built-up areas and open space (which isn't great to start with) gets more and more indistinct as well.