Hello bolegna,
Which coordinate system you are selecting on export? Can you post a couple of lines from the OBJ file with the coordinates of the vertices?
It looks like some projected coordinate system (for example, UTM projection) has been used, where the values of X and Y are millions of meters, but the 3D modelling application doesn't support so big values, keeping the coordinates as float type, thus truncating the smaller bits.
If it is the case you can try to use Local Coordinates on export, or use Shift values in the export dialog to subtract large values from X and Y coordinates.