The DB_REF definitions in QGIS are wrong (at least in QGIS2).

They are missing any +towgs84 parameter, which is necessary for the DHDN datum.

Instead of EPSG:5683, take EPSG:31467 which has the correct datum shift values.

The linked document lists datum shift values that differ from EPSG:31467, so you might use these PROJ strings instead:

For GK2:

+proj=tmerc +lat_0=0 +lon_0=6 +k=1 +x_0=2500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

For GK3:

+proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

For GK4:

+proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=4500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

Comparing with datum transformations with BEAT2007 and EPSG:31466, DB_REF is about half way between them. Beta207 is 1.2 meters away, ESPG:31466 0.5 meters.

The DB_REF definitions in QGIS are wrong (at least in QGIS2).

They are missing any +towgs84 parameter, which is necessary for the DHDN datum.

Instead of EPSG:5683, take EPSG:31467 which has the correct datum shift values.

The linked document lists datum shift values that differ from EPSG:31467, so you might use these PROJ strings instead:

For GK2:

+proj=tmerc +lat_0=0 +lon_0=6 +k=1 +x_0=2500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

For GK3:

+proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

For GK4:

+proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=4500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

Comparing with datum transformations with BETA2007 and EPSG:31466, DB_REF is about half way between them. BETA2007 is 1.2 meters away, ESPG:31466 0.5 meters.

The DB_REF definitions in QGIS are wrong (at least in QGIS2).

They are missing any +towgs84 parameter, which is necessary for the DHDN datum.

Instead of EPSG:5683, take EPSG:31467 which has the correct datum shift values.

The DB_REF definitions in QGIS are wrong (at least in QGIS2).

They are missing any +towgs84 parameter, which is necessary for the DHDN datum.

Instead of EPSG:5683, take EPSG:31467 which has the correct datum shift values.

The linked document lists datum shift values that differ from EPSG:31467, so you might use these PROJ strings instead:

For GK2:

+proj=tmerc +lat_0=0 +lon_0=6 +k=1 +x_0=2500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

For GK3:

+proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

For GK4:

+proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=4500000 +y_0=0 +ellps=bessel +towgs84=584.9636,107.7175,413.8067,1.1155214628,0.2824339890,-3.1384490633,7.992235 +units=m +no_defs

Comparing with datum transformations with BEAT2007 and EPSG:31466, DB_REF is about half way between them. Beta207 is 1.2 meters away, ESPG:31466 0.5 meters.