I recently went and collected some waypoints with a GPS that is in NAD27 UTM16N. After uploading the GPX file into QGIS, I saved it as an ESRI shapefile, and changed the CRS from WGS84 to NAD27 UTM16N. After adding it to a new file, the coordinates appeared to be in the correct place, but after comparing them to the points in the actual GPS, it appears that everything has been slightly shifted. Using one point as an example, in the GPS it is X = 327398 Y = 1836319, but in QGIS it is X = 327401 Y = 1836410.
Finding this strange, I tried using the 'Project' tool in ArcMap to convert the GPX from WGS84 to NAD27 UTM16N. Using this method, my points have the same coordinates as in the GPS.
Does anyone know how to solve this issue in QGIS, or have any insight as to why the coordinates for points are not matching up?