They don't have the speed or the flight to keep up. Wonder Man would give a good fight, but he'd be overpowered eventually. Herc is too slow to be able to take advantage of his strength. Atlas apparently (i haven't got the issue yet) took out Hyperion in NT #16 by stomping him, but something like that would only happen in a comic.
Meanwhile the X-Team are completely curbstomped.
JLA with ease.
Astounding amazing ease.
It would actually be better if the 2 Marvel teams were mixed together, and even then the JLA would have the better odds.
And let me explain.
You have Superman, WonderWoman and Captain Marvel.
Each of them is amazingly strong .....stronger than 100ton lifting capacity (which is usually employed by Marvel while DC has a far higher lifting ability for its characters ....Superman has been estimated at over 800,000 tons in the Death of Superman arc, and in some writings ....note post-crisis, thus not even his uber-strong pre-crisis levels ....he has been shown as stronger for example when he, WW, and MM pulled the earth's moon. Note this was post-crisis ....pre-crisis he was juggling planets. Thus he is over the 100 tons Marvel levels easily).
They are also EXTREMELY fast.
And one of them (Superman) has a wide variety of powers, while the other two are powered with godly attributes.
And they are facing off against the following:
Avengers
Atlas
Hercules
Wonder Man
and
X-Men
Cannonball
Colossus
Warpath
The Avengers for one are earth-bound, apart from WonderMan.
The X-men also have some issues, for example Colossus. He has lifting ability around 100tons, which is ludicrous when compared to Superman/WW/CM.
The biggest threat would be CannonBall, but as someone said all that would be needed is for them to rough him up until he stops blasting, and then he is just another mortal in the presence of gods.