Since the polls are up I suppose I should take a crack at this one since no one else has.
Both of these guys have multiple things in common. Both were primarily heels during their heyday, both were multiple time world champions, and both were big stars. Despite that I'm leaning towards Kiniski because of the quality of his feuds, matches, and longevity. Was Kevin Nash really remembered for being a champion, or was he more remembered for stunts like ending Goldberg's streak or the finger poke of doom? Seemed like the people that he rode with defined him more than he actually did himself.
Kiniski was Canada's self proclaimed greatest athlete and had several noteworthy feuds with the big names of his time like Sammartino, Carpentier, and Killer Kowalski while working his way up. And he finally achieved the biggest prize at the time - the NWA title, and he went through Lou Thesz - the biggest star at the time in order to do so. And he held that title for over 1100 days and defended it regularly against every big name in the industry in the different territories as the biggest heel of his era. The man just couldn't be stopped.
Nash's title reigns came and went as fast as he'd win them. 97 days total he spent as WCW champion, and most of his reigns came in 1999 when the company started going down hill. From his second title reign to his fifth title reign there wasn't a single champion that could hold the belt longer than 2 months because the belt got hot potattoed so often. And it's arguable that Wolfpack Big Sexy was more relevant as a star than Big Daddy Cool Diesel.
Unlike Nash, Kiniski was built up to be a force to be reckoned with. He was the man to beat in the industry, and for years no one really could. Even after his monumental reign Kiniski still went on to wrestle prominently throughout the US and Canada. He became a promoter and helped turn Vancouver into a financial hotbed. Nash made some appearances in the WWE here and there, but nothing notable.
Gene Kiniski should be the winner here. He was the bigger star, had a bigger legacy, and had more impact on the business as a whole. Nash was part of two groups that were both bigger than he was, and he was not really the standout of either.
For that I'm voting "Canada's greatest athlete" Gene Kiniski.