Neither of these fellas can do nothing to kill the other. Juggernaut would be receiving constant beating due to Doomsday's speed and strength advantage, yet it wouldn't kill him, though. DD could still BFR Juggy. Juggy doesn't have anything against DD, he wouldn't be even able to touch him. Not even counting the fact that DD has already received a beating from Superman who is definitely stronger (and faster) than Juggernaut. Therefore DD has evolved a way past the level of physical beating Juggernaut could ever give him.
Juggernaut is indeed almost completely invulnerable to physical attacks. However, if someone like Living Tribunal (or Eternity, for example) turned all his might into a punch, Juggernaut would seize to exist at that very moment.
It's bullshit if Juggernaut has somehow managed to resist Eternity. Where Juggernaut gets his powers isn't even close to Eternity.