The Thing vs. Juggernaut is going to result the same way it would if ANYBODY besides the Hulk decided to go 1-1 with Juggernaut.
The Thing and Juggernaut like most the heavyweights in the Marvel Universe, have about the same Strength class. I believe that the Thing is a bit weaker that Juggy and the Hulk, but the difference is not enough to have an impact on the fight.
Juggernaut and Thing come out swinging. They both exchange heavy hits for about an hour and then Thing gets too tired to continue. The Thing has nothing but rockhard skin and super-strength. This is not going to do well against somebody like Juggernaut, who has rock-hard skin and super-strenght, plus physical invulnerability and infinite endurance.
The cards are just too stacked against Thing for him to win in a slugfest against Juggernaut.
In my opinion, the only person who has the ability to successfully take on the Juggernaut in a slugfest is the Hulk, and even so, that battle would most likely end in a draw.
By the way, currently, there is issue #1 and #2 of "The Hulk vs The Thing: Hard knocks" on shelves. Basically, the Thing claims to have beaten the Hulk before. If any of you want to Argue that the thing can tango with the Hulk and thusly, the THing can tango with the Juggernaut, you're wrong. The Thing can hold his own against the Juggernaut, but not for long. The Hulk gains strength too fast and The Thing can't keep up. The Thing has even admitted in one comic where He and the Hulk fought for a charity auction.
"This just reminded me..if I was ever in the same league as the Hulk, I'm not anymore."