Inoki has won championships in the USA, so before anyone goes down that alley, lets shoot it down there. He also managed to do something Bret Hart couldn't, and that is beat Bob Backlund. Bob Backlund was well into his forties when he beat Hart, but he was in his prime and the midst of a seven year title reign when Inoki beat him.
Inoki's long and succesful MMA career shouldn't necessariky put him over, but it should suggest that he has the mat skills to go toe to toe with Hart.
Hart's prime was most definitely 1992-97, and if we look at that time, he wasn't really beating the big names of the era. In his first reign as champion, he beat Papa Shango, a young HBK and Razor Ramon. The megastar of the era, Hulk Hogan, was not faced. He was then dominated by Yokozuna, and lost the championship.
I don't want to go into an exhaustive history of Bret Hart, but he won the title back, because Yokozuna fucked up, but in 1994, his only significant win bar the Royal Rumble win was against Owen in a cage, who had beat him at WrestleMania. In 1995, he was feuding with people like Hakushi, Isaac Yankem and Jean-Pierre Lafitte.
My point is this, Hart was great and all, but he never really got the big win in his WWE career, he thrived in an era with no megastars, but without becoming a megastar himself. Then he went to WCW, where there was megastars but never really picked up serious momentum.
On the other hand, Inoki beat just about all of the big names in global wrestling that were around. I'd probably rather watch Hart, but I think Inoki nwould win a match between the two.