According to the specs, the Genos will use the same Style Format SFF and SFF2 (GE). Thus the styles from the Genos can work when they are copied to the S970. However, they will sound completely different, since the S970 has much fewer DSPs and the S970 will use substitutes for voices not available. So this will not gain any positive effect. Better use the old styles that were made specifically for the S970.
And no, no voices can be moved from one keyboard model to another.
You are correct, however having almost 600 new Genos styles, with top Yamaha style programming, would be a wonderful resource of new styles for your older PSR or Tyros model. A few would require re-voicing (or Drum Kit change) and maybe experiment with a different DSP effect if the default one isn't suitable. If a new Genos style featured a brand new Mega voice for a style part, an equivalent S970 Mega voice would sound fine in most cases and also take advantage of the Mega programming and hidden sub-channels in the style.
The Genos also introduced a couple hundred new Multipads, just re-voice as needed as you copy them over to your S970. If I decide on a Genos, upgrading one of my Tyros 5s with modified Genos styles and multipads would make the upgrade transition more subtle. Just as copies of styles and Multipads get posted from previous Yamaha keyboards, the new Genos Styles and Multipads will eventually get posted.
I picked up nice brand new styles copied over from some of the newer CVP Yamaha models, including a couple of Freeplay styles not on my Tyros 5. Actually I can make them sound better on a Tyros 5 then the original keyboard they are from (T5 Real Reverb DSP for an example). Most were picked up in the resource section of this forum.
Like I stated in another thread, if one was to argue that the Genos has 40% new content over a Tyros 5, a lot of the new Genos styles and multipads can be backwards compatible to the Tyros making the difference more like 25%. I consider everything before deciding on the Genos or wait for the next model. Funny how the S970 and Tyros 5 can eventually play "all" of the Genos styles, but the Genos cannot play the unique Audio Styles found on the S970/Tyros 5. Still not sure if Yamaha is going to convert the S970/Tyros 5 factory audio styles to Revo kits, but it is confirmed that the Audio style expansion packs will be converted.
Marcus