I think I will give this to Mario. Physically he is far superior to Eggman. Sure, with all his machines he can have ways to defeat Mario, but he will have no way of knowing the true threat level Mario poses. He will just see him as a man challenging him without knowing that Mario has powers and abilities on par with Sonic. If all of Robotnik's machines are lying around in Central Park, it's up to pure chance which one Robotnik will use first, and as long as Mario has the Pure Hearts, only the very best of the scientist's devices would be able to deal with him. At least 6 times out of 10, Robotnik would first go for something that only posed a minor threat to Mario, and as soon as Mario got past it, he would deliver a blow to Robotnik. Durable as Robotnik is, even one blow from Mario should be enough to incapacitate him unless he severely holds back. Mario has Galaxy level AP at minimum, while Robotnik's physical durability is "only" Small Star level at best. Mario is definitely more skilled than the doctor, so it shouldn't be that hard to land one blow. While there are definitely scenarios where the machine Robotnik goes for at the start could catch Mario by surprise and take him out, I imagine that the majority of the outcomes would be the opposite. If Robotnik had some preparation time, he would probably have a pretty good chance at victory, but this seems to be a random encounter battle.