I've been using OsmAnd primarily for a few months. Some areas that it's fallen short, and forced me back to Google: unreliable and slow public transport directions, terrible default routing engine (solvable), lack of up to date local business information, search that can't find basic street addresses, no updates on road closures.

Organic Maps looks great, I'm going to give it a try and see if it solves any of these issues.

There's an app called StreetComplete (recently discussed on HN) that allows you to easily contribute missing information like local business information to OSM. If you can find the time, you can use that to solve some of the issues you have and help others at the same time! :)

repository: https://github.com/streetcomplete/StreetComplete