Quite possibly DDD, after all Mario and DK mainly just shifted their, shall we say riverly, from the more violent aspects to more peaceful competitions.
Donkey Kong pited mario and DK up agaist one another, as did mario and DK, in a way that seemed like they were life long enemies. Mario Kart, Mario Party(the first few), Super Smash Bros. also put those two(and others) against one another, but in more of a "who is the best" kind of way. I can easily see Mario and Sonic going the same way.