The two boards have many things in common, including the operating system and most of the same samples. I'm pretty sure that if you put an S770 and an S970 side by side, and played the same voice / style on both, you would be hard pushed to tell the difference.
I think the main differences are that the S970 has ...
.. more panel voices
.. more panel styles (not a big deal since you can find them all on this site)
.. more expansion memory
.. the 'euro organ' sample in Organ Flutes
.. better onboard speakers
.. vocal harmony
.. audio styles
The last two are the only real functional differences.