As this is Hal Jordan as Parallax, he was at his most powerful (prior to the image displayed above which appears to suggest that it is from the time of the 'Final Night' storyline) capable of massive matter and energy manipulation (including time manipulation) having the power of the entire GL storage battery on Oa. That's enough power for the entire GL corps (7200 members strong + additonal GL agents). With the power levels displayed in Zero Hour and Final Night, I think that Parallax would win out.
"Hey Creator do you know the issue of Green Lantern when he fights the Justice League and Kyle with the Power Ring then it finishes with Ganthet giving him more power and him sitting on a rock by himself?
Sorry Ace, don't know off the top of my head (I am still at work).
"This fight would leave alot of whichever universe in dead. I don't think either of them has an edge over the other.
This Thor is a galaxy buster. He should be on the level of one cause everytime Odin had his odin force he destroyed galaxies while fighting foes. But I doubt the fight would go in such a way besides that this Thor wouldn't be able to take down that much of the universe on the same level as parallax.