- Address search. OSM has lousy address coverage.
- One single provider, works out of the box. OSM is much more flexible in the long run, but you can't just plug in an "OpenStreetMap API" and expect it to do everything for you. (That said, Mapbox is going a long way towards providing this.)
- Satellite imagery. (Again, you can get this from a reseller like Mapbox.)
- StreetView.
- Public transport directions.
- Familiarity.
Have a look at Germany in OSM. That's what crowdsourced maps can do.
You also see Google talking about extracting building numbers from Streetview photos.
* Telnav Scout: a typical GPS/navigation app. I guess figure using OpenStreetMaps is better than their proprietary data, and they don't want to be competing with Google and depending on Google for data at the same time.
* Humanitarian Organizations (HOT): it turns out that you can get volunteers to trace maps from satellite imagery for remote places that have no other maps.
* Backcountry/mountaineering: a lot of places in the mountains are poorly mapped in Google Maps. OSM is a lot easier to edit, and supports a lot more features when it comes to describing terrain and whatnot.
Disclosure: I work for Mapbox, we offer a directions service based on OSRM, I'm paid to work on it daily.