I played around with a bit more today. It would appear the customZoomLevelSet as in the sample fixes the issue with OpenStreetMapOverlay for both iOS and Android -- features appear exactly where they should. Maybe this is a different issue but in order to get and OSM maps to display I have to use the same zoom customZoomLevelSet for the main map.
With the OpenStreetMapLayer and CustomZoomLevelSet from the sample there is a discrepancy between the OSM map and features drawn to the map. However using the OpenStreetZoomLevelSet for the OSMLayer fixes that problem.
So at this point the only issue I really have is the speed in android. If I use the same zoomLevelSet for the OSMLayer and the map view the speed is almost as fast as using the OSMOverlay. Using a different zoom level set for the map view is apparently causing the speed problem.
The speed problem does not occur with iOS.
Attached is a android project that show the speed issue I am encountering -- I removed the projects .mapsuitelicense file so that has to be added back in.
gettingStartedAndroid.zip (73.5 KB)