New 52 Superman vs Batman
Batman wins. He would simply be too powerful with the Green Lantern ring. In fact I remember it being said that he would be the most powerful Lantern ever.
Batman would be no more powerful than Hal Jordan, Alan Scott, Guy Gardner, or Kyle Rayner, who are the five main Green Lanterns in the comics. And I'm pretty sure Superman can beat all of them.
Actually he would be more powerful because DC has made public statements stating that he would be.
New 52 both I assume? unfair to pair Pre 52 Batman against New 52 supes since one has got many more feats than the other. In any case, there is a reason why Hal was chosen as the Green Lantern, his will is the strongest on earth. Batman would not be a better GL than Hal merely because his will (while formidable) is not as immense as Hal's.
OP never specified which versions, either way it matters little as both New 52 Supes along with Pre- 52 Supes could beat the strongest of the Green Lanterns, so whichever version Clark should still win.
Unless Batman can use the ring to make Kryptonite. I've seen Hal and others do it before, but some on this site have argued that's it's not legible. Either way if the ring is capable of doing this, Batman would win as he can fall back on the rings other abilities to play defense/keep away while the Kryptonite slowly kills Supes.
It is the current versions per Battle Forum rules of non-specification.
New 52 Batman can make Superman bleed. If you add the Green Lantern ring to the mix, Batman would control the fight.
100%, completely, absolutely FALSE. Intelligence he's probably superior in, but that matters little when using a Green Lantern ring. Willpower and creativity are the needed factors, something the 5 main Green Lanterns are superior to Batman in.
No way, Batman's willpower has demonstratively been proven to be superior to the main 4 Lanterns, perhaps not Alan Scott.
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