I don't know a lot about the European datums, but going from an old local to a recent world datum will offer many variations. Generally when going from a larger datum to a small datum the positions will shift towards 0,0. This may be more coincidental, I haven't worked out the math myself. Also, the terms GRS80 and WGS84 are not interchangeable, though the variations are insignificant for most applications.
You can look up the details of the 7-parameter transformation in your documentation if you want some hard numbers. The XYZ shift for your transformation is this -89.5, -93.8, -123.1.