I’ll give my opinions now:
I believe that the Justice League would probably win such a fight, but not as easily as many would think.
Let’s face it, Superman is…well…Superman, but let’s not forget that he is vulnerable to two things: Kryptonite and magic. Thor is a god, who uses magic. I think that although Superman is a more powerful hero than Thor, Thor could definitely give Superman some trouble.
Batman is just amazing, and as much as I love Captain America, he wouldn’t really stand too much of a chance against him. The only Avenger that I think could stand a chance against Batman would be Iron Man. Iron man is a human fighter jet. And even Batman would have some trouble with him.
I’m not really sure who The Hulk’s DC counterpart would be, but the Hulk is basically a small Godzilla. He would give every member of the JL a tough time in my opinion.
The Green Lantern vs. Iron Man would be a really interesting fight. I’m not sure who would come out on top. (probably the Lantern)
Wonder Woman vs. Black Widow is another interesting scenario. The Black Widow is basically a female Batman, and has hand-to-hand combat skills similar to those of Wonder Woman.
The Green Arrow vs. Hawkeye is perhaps the most difficult to judge. They’re both practically identical when it comes to skill and ingenuity with a bow and arrow.
Hawkman, Ant Man, Aquaman, and the Wasp all pretty much suck, let’s be honest.
And finally, for the JL, you have Martian Manhunter and Cyborg, who are both really cool. And for the Avengers, you have the whole S.H.I.E.L.D organization as well as the Red Hulk (in post-Hulk Avengers comics).
I think that the sheer power behind the JL’s members would give them an edge over the Avengers, but I don’t think it would be very easy. The Avengers are pretty amazing as well.
Realistically, Superman would be enough to handle the Avengers...
No. Just no. I would agree with this statement if Superman didn't have two terrible weaknesses; Kryptonite and magic. Bruce Banner is going to have some Kryptonite on hand, and Thor is a frickin' Norse god lol. Superman would not roll over the Avengers.