Not sure if that's really relevant to the quality of the apps themselves.
Since everything (at least by default) through F-Droid is FOSS, there is a significant lack of ads and other misfeatures. Apps that depend on an account with a non-free third-party service are clearly marked as such. Most apps aren't foolishly tied at the hip to Google Play Services. Malware is non-existent.
I know of many such stores. Usually they are proxies: They download the app from the Google store, you download it from the proxy. The question is, how do you know they haven't inserted malware? It seems like a very obvious vector for attack. You could authenticate signatures or hashes, but where do you find the authoritative signature/hash?
For those interested in taking a shot at using these services, here are a couple of the more credible ones I've run into in the last couple years (I haven't used them in at least 6 months, so possibly their status has changed). Use at your own risk!:
- APK Downloader: By someone on XDA-forums, a leading Android dev community. It comes in several versions and forks by other XDA members, and for several platforms. I don't have time to sort them out now, sorry. Beware of malware-infected hosted implementations.
