Hi Luluc,
From my experience, factory styles would usually only sound authentic and correct for the instrument it was designed for, even if they also feature in other models. For example, even if all the tracks are present, the effects may differ or may not even be present in the instrument (like in the case of G1 vs G2 effects), which would alter it's intended sound.
So to answer your question, I would probably stick with using the Genos1 version of the style even if its present in Genos2 because there will always be some differences and you would almost always need to tweak it which I would find pointless if you already have the same style in the G1.
Hope this makes sense.
Danny.