I was going to say, Firestorm’s currently dead.
It isn’t a contest.
The Justice League are winners. The Watchmen are losers. That’s all there is to it.
Wouldn’t the Justice League’s having Captain Atom cancel out Dr. Manhattan?
Doc Manhattan’s ultimately based on Captain Atom, but he was the most changed of the Charlton characters (aside from Nightshade, whose equivalent was really a Phantom Lady/Black Canary clone).
Atom’s powers are nowhere near Manhattan’s level - as I said, it’s Firestorm who’s the DCU character with the closest power set, though the number of high powered sorcerers make that moot.
Look at it this way: any one of the Justice Leaguers (Green Arrow aside) can likely take out all of the Watchmen (Manhattan aside). Then you’re left with at least 5 superpowered folks (the usual Superman, Wonder Woman, Martian Manhunter, Green Lantern and 2 others you can pick) against an apathetic demi-god. Assuming Manhatten gets riled up he could do a lot of damage, but the odds of him getting personally involved are pretty low.
For extremely large values of 5, no doubt.
Assuming the Watchmen team is from their Crimebusters heyday, prior to Manhattan discovering the joys of apathy:
All but Doc. Manhattan go down, taking a couple of Leaguers with 'em.
Manhattan, enraged at the death of Silk Spectre II, divides into 5,000,000 Doc. Manhattans and (glowing blue) dick slaps the JL to a pulp.
Why would he be? Structurally, there’s no discernable difference between a live body and a dead body.
It’s harder to boink the dead one, and that’s one of the few things Manhattan still cares about.
That being said, Manhattan isn’t quite an irresistible force (he didn’t have the capacity to destroy all Soviet nukes in the event of a mass launch, or so he claimed).
This one is mostly easy. Nite-Owl is a poor man’s Blue Beetle. Except for Dr Manhattan, the rest of the Watchmen characters aren’t even superpowered (nor have the tech to catch up)–and they’re not even a team!
That said, Dr Manhattan may be more powerful than the JL put together. Unless they bring J’onn J’onzz &/or Zatanna. But since Dr Manhattan is deeply mentally ill, a fatalist depressive who cares about very little, it’s hard to say if he’d bother. I guess he would if the writer said he would.
Oh, Detroit? Detroit League would win. Jon could see Gypsy even while she’s invisible & several minutes before she arrived; this would distract him.
Then J’onn would show up & do to Jon what he did to Despero. Then Vixen & Steel would pwn the rest of them.
Bats has 7 stone on Rorschach
I think Bruce would win that fight.
And the JL Europe was once led by Captain Atom, the model for Dr Manhattan (though admittedly Nathaniel Adam is less over the top than Jon is).
OK, Tengu covered that.
We’ll bring in the Wonder Twins–They fight as one! (Yes, I know they’re technically Super Friends/Extreme Justice/Young Justice, depending on the version.)
Martian Manhunter is a telepath.
I’m betting he can take Manhattan.
Let the Flash & Green Arrow mop up the rest like mud off the garage floor.
If he can be arsed, Manhattan paints the walls with the Justice League. But only if he sees that he did it in the future. One of the advantages of squaring off against a determinist.
[missed the edit…continuing the thought]
This is after all, a man who can tell you how things are going to go down and still be genuinely surprised when they do.
Watchmen would eventually be toast, but I suspect Ozzy will somehow trick Superman into a cryptonite barrel at the bottom of the sea before getting blown away, he is sneaky like that.
We all know what happens. Superman punchs Dr Manhattan, irradiates Kansas, and retires in guilt for a couple of decades.
Poor Captain Marvel … 
Jon’s the precognitive guy who can make fire, right?
And, AFAICT, Dan is the guy who can drop Gypsy and Vibe and Steel and Vixen and Aquaman, provided they’re at their 1985 levels and he’s working that sonic weaponry from behind all that armor plate with his goggles on; he’s like a low-budget Iron Man, but that’s still pretty good. (And anyone who isn’t bulletproof needs to be faster than Eddie Blake or else take a gunshot to the eye.)