i think bowser would win because hes a lot bigger and stronger. also you know hes stronger cause mario has to grab him by the tail and swing him into bombs while for eggman you just jump on him so that makes dr. eggman way weaker.
bowser knows how to take a hit, Seeming you throw him into lava, bombs ect and eggman only has liek machine gun, and explosives, so yea bowser would just like pick egg man up out of his floating chair and gobble him down.
Bowser becuase bowser is bigger,stronger and can breathe fire.Also becuase eggman is weak without his robots and machines.Also bowsers jumps can can send eggman to space.