Compuser10165 :
Maybe in the not so distant future, neither of the technologies will be supported, and instead implemented a new open standard (something between the two) with no proprietary company but I don't know about the likelihood of that.
AdaptiveSync is already an open standard: an official VESA extension of the DP 1.2 spec.
FreeSync is just an AMD branding initiative to give themselves control over marketing - allow only the displays that meet AMD's requirements to market themselves as FreeSync when technically, any display that meets the FreeSync spec will also work without the manufacturers having to pay AMD's trademark toll.
Nvidia could just as easily implement their own AdaptiveSync support, either as generic AdaptiveSync support as AMD should have done or trademarked under their own house-brand to further confuddle the market like AMD did.
IMO, the FreeSync brand made things more confusing than they should have been. As far as AdaptiveSync displays are concerned, it means nothing more than "AMD-Approved."