The Aurora Store app is just a frontend for the play store. It's a useful tool, but gives none of the benefits the existence of F-Droid provides to the world. Obtainium just fetches an .apk from a site, also useful, but provides none of the security aspects of F-Droid or the Play Store.

There is no good alternative to F-Droid. Thankfully that's just because it is such a great concept.