Does anybody know if the new Osmo will use the same batteries as the current model? I have three or four batteries for mine, and while I'm keen on upgrading to the new version, I don't want to have to buy so many new batteries...

The osmo+ uses a higher capacity 1225mAh battery with a voltage of 11.55volts. (Osmo 980mAh and 11.1 volts)
It is the same dimensions as the osmo's battery. As for using the osmo smaller capacity battery in the osmo+ im not sure,I can't see why not, It wouldn't last as long as the osmo+ battery.