Your Gauss-Krueger projection uses `+datum=potsdam`. Up to 2012, this was hard coded in proj4 to a very unprecise value using a 3-parameter-transformation.

You find more exact values for 7-parameter transformations in this topic:

http://forum.openstreetmap.org/viewtopic.php?id=12723

There is an even better ntv2-grid transformation available [here (take the binary)][1], that has to be in the same folder as your application and data, unlsss you specify full pathnames.

To compare the different possible values, I made this test batch file:

    echo epsg31467-epsg4326 >out.txt
    cs2cs +init=epsg:31467 +to +init=epsg:4326 31467.txt >>out.txt
    
    echo proj-Definition epsg >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +datum=potsdam +units=m +no_defs  +to +init=epsg:4326 31467.txt >>out.txt
    
    echo proj-definition Qgis >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=582,105,414,1.04,0.35,-3.08,8.3 +units=m +no_defs +to +init=epsg:4326 31467.txt >>out.txt
    
    echo proj-definition nadgrid >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +x_0=3500000 +y_0=0 +k=1.000000 +ellps=bessel +units=m +nadgrids=./BETA2007.gsb +wktext +to +init=epsg:4326 31467.txt >>out.txt
    
    echo epsg31467-epsg3785 >>out.txt
    cs2cs +init=epsg:31467 +to +init=epsg:3785 31467.txt >>out.txt
    echo proj-definition Qgis >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=582,105,414,1.04,0.35,-3.08,8.3 +units=m +no_defs +to +init=epsg:3785 31467.txt >>out.txt
    
    echo proj-definition nadgrid >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +x_0=3500000 +y_0=0 +k=1.000000 +ellps=bessel +units=m +nadgrids=./BETA2007.gsb +wktext +to +init=epsg:3785 31467.txt >>out.txt
    
    echo epsg31467-epsg3857 >>out.txt
    cs2cs +init=epsg:31467 +to +init=epsg:3857 31467.txt >>out.txt
    echo proj-definition Qgis >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=582,105,414,1.04,0.35,-3.08,8.3 +units=m +no_defs +to +init=epsg:3857 31467.txt >>out.txt
    
    echo epsg31467-epsg900913 >>out.txt
    cs2cs +init=epsg:31467 +to +init=epsg:900913 31467.txt >>out.txt
    echo epsg31467-proj900913 >>out.txt
    cs2cs +init=epsg:31467 +to +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext +over +no_defs 31467.txt >>out.txt
    echo proj31467-proj900913 >>out.txt
    cs2cs +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=582,105,414,1.04,0.35,-3.08,8.3 +units=m +no_defs +to +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext +over +no_defs 31467.txt >>out.txt

with any sample Gauss-Krüger lon-lat coordinate pair in 31467.txt


  [1]: http://crs.bkg.bund.de/crseu/crs/descrtrans/BeTA/de_dhdn2etrs_beta.php