Mapbox is built on OSM data and has pretty nice styling. Gaia GPS is one app that provides (among many other things) Mapbox layers on iOS and Android.

Hehe, I had just edited my comment to mention Mapbox, then I noticed your reply. :)

> Mapbox Streets is an example of good map design: https://www.mapbox.com/maps/streets/

Hmm, doesn't show forests and doesn't show built-up areas, either, which are precisely the things I really dislike about Google's map design, too.