Basically, when Miyamoto showed Yamauchi Yoshi's Island for the first time, a game that he had been laboring over for two-three years, the big boss was less than impressed. Yamamuch then pointed towards Donkey Kong Country, which was in mid development ,and which he was totally enamored with, stating that it was the direction that they should be going., And then he told Miyamoto to make YI less cartoony. Feeling a bit insulted, he told his team to make it even more child-like.
But by the time it was all said and done, like veen mentioned, it was past the point of serious interest for most, perhaps even Yamauchi, hence why he probably let it pass by despite his objections to the art style. Or maybe he was impressed by being proven wrong.
Miyamoto has actually been quoted as saying, something to the effect that, Donkey Kong County is simply proof that many people will often play a game just because of pretty graphics, and be fooled into thinking that might possibly good, even when its clearly not. And as far as I know, that's the only time that the normally very upbeat and positive guy has ever been negative towards a specific game.
So I wouldn't say it was a total redesign when it came to gameplay, just the graphics.
