The thing is, Supes and Majestic aren't going to be a factor in this fight until the other one is down for the count. Neither one can afford to attack anyone else and leave the other one free to destroy their team. And, after they win, that means a huge advantage for the winners team.
In this case, I don't think Majestic will be that exhausted after beating Supes. Superman just slugs it out with an opponent until they fall over. He'll block a few punches, sure, but for the most part his focus is knocking his opponent down. Majestic is different, he doesn't hesitate to use every advantage he has. He goes straight to super speed, hits his opponent with enough strength to take them down in the first few blows.
Majestic is the better and stronger fighter. Even if he is tired after beating Superman, an slightly weakened Majestic is better than almost anyone else on your team. Hellboy's stone hand only does extra damage to supernatural creatures, since Majestic isn't supernatural that hand isn't going to do any damage. Spawn is strong, but like Corlock said, Majestic would not hesitate to decapitate him.
Mignighter has fought dozens of super powered opponents at a time, he could probably take Nightwing and Grifter on by himself. With Daredevil backing him up, he would be almost unstoppable.
Hawksmoor versus Spider man woudl be interesting. But, since Jack can tell the buildings not to cooperate with Spiderman and can phase through the streets and walls, I think he wins eventually. Jenny versus Dark Claw would be ridiculous. It would just be an endless cycle of shocking him, waiting in pure energy form until he gets up, and shocking him again until Jack could phase him into the street.
Either way, Black Bolt and Jenny could both move between your team and mine, and hit the other team with voice and lightning right as the fight starts while the two everymen are duking it out up above. Those who survive that first blast could be mopped up by the rest of the team.