@Robert-Laudensack, 4.4.0 (404) is the latest beta that has also gone to public. So if currently, if you do a re-install, not matter if you are beta or not, you get build 404 from the Google Play Store. So both your phone run the same version. So I doubt it is version related, it's probably more phone related.
You could try to install an older version, to check if that indeed works without problem, but for that you will have to resort to an alternative Play Store like "Aptoide". Be sure to completely remove a newer version before you do. It will only offer public versions though (the previous being 4.3.9 - 395)