I have two layers, one in ESPG:4616 (JGD2000) and one in ESPG:30165 (Tokyo, Japan Plane Rectangular CS V). In QGIS, layer are not matching as you can see below.
I tried everything in QGIS, modifying the project projection, with and without "on the fly", recording the layers in another coordinate system, etc. At this point, I through that the problem came from the data.
However, when I open both the layers in ArcGIS, the software do an automatic transformation (one projection into one another) and layers are matching as you can see below.
At this point I am lost, I even tried to record both the layers in a brand new projection in ArcGIS, still layers are not matching in QGIS.
Here is a link with a small sample of both layers
ArcGIS also has a problem, when I add a basemap, we can see that both layers are not overlapping
While using open layer in QGIS, one layer is overlapping the background map.