The SNES and Genesis were really close in the West, Sega just had no presence in Japan. And I speak as someone who actually was old enough to remember that era well, lol. Awesome time to be a gamer.
To say one "dominated" the other is silly.
The only real dominant platforms have been IMO, the NES, the Playstation, the Playstation 2, Game Boy/GBC, and Nintendo DS.