Juggernaut wins. Juggernauts power is derived from his possessing the Cytorrak Gem. Batman beats guys like Superman due to PIS. Omg. I just happen to have a batarang here made of kryptonite... Whatever.. In any case Batman is the essentially the God of Science. But what could science ever do to Juggernaut. Only Psionics have ever really affected him. And Batman is not martian manhunter or aquaman...
Essentially Batman would pass out from exhaustion from trying to dodge Juggernaut for two weeks. Batman's only hope for a win would be a BFR. He would not be able to hurt Juggernaut. Not classic anyways.
*laughs* Batman one million steals his soul, and then takes the hollow body of cain marko into his lab for extensive testing.
However, to the poster who mentioned bane, PLEASE!
Jesus, bain is a CLASS TWO villain, Juggernaut is a CLASS 100! Bain is NOTHING like Juggernaut.
Regular batman would lose to Juggernaut without some heavy one sided prep (or motherbox rubbish), but Batman one million could take him.