They would probably fit in about as they always do in these settings. Which is that they still managed to pull their own weight, in or out of a fight. Sure, it might take some creativity for Batman to take down an enemy that Superman would be able to handle easily, but that makes the fight far more interesting. The pulpier heroes are also usually the ones who are good at things like investigation or otherwise learning what the group really needs to know. While the powerful types are running off to fight, the pulpier guys are usually either sneaking past that same fight or otherwise doing something to help the team big-time.
And, of course, not every villain or threat will be some world-ending one. Sometimes, it's just a bank robbery or other incident. Not to say that pulp-styled heroes are somehow stuck with "small time" stuff.