Two magnificent "What If" scenariors present themselves in these hypothetical battles, the first betweeen the Justice Society of America and the Invaders, and the second pitting the Justice League of America versus the Avengers. While the mainstream Marvel Universe, known as Earth-616, existed concurrent with the original DC Multiverse, it was only have DC's five core realities merged into one singular Earth that the actual denizens of Marvel met their analogues at DC. And given the magnitude of metahumans on Earth-616, it would take a New Earth filled with such DC stalwarts to ward them off. In the case of the Invaders and the JSA, the shear number of Socialites would simply overwhelm Captain America's crew, not to mention the tremendous power of several of the Society's individual members. Not pictured here are Superman, Spectre, Doctor Fate, Johnny Thunder's Thunderbolt, all able to level the playing field!
As for a matchup between the Justice League and the Avengers in the 1960's, well this would be a bit more problematic for both teams of titans. The quartets herein pictured would make for an interesting matchup indeed, and the varying abilities of the elemental/gigantic/armored and agile foursome of the Avengers would cause a challenge for the metamorphic/swift/energetic and amazing fantastic four of this particular League. When considering the full assemblage of the Avengers versus the League, especially in their post-Satellite era, when both teams nearly recruited the entirety of their Earth's elites, the matchup proves exceedingly daunting for each. Strengths on one team, such as the League's seemingly limitless potential i.e. Superman's strength and Flash's speed, are matched by the weaknesses these same characters manifest such as Superman's aversion to Kryptonite and Green Lantern's ring toward the color yellow. For the Avengers, what you see is what you get, and while all of them... save perhaps for the Hulk... seem to have caps on their abilities, they also do not have the hindrances of their peers over at their Distinctive Competitor.
And so, as the Marvel Universe breaks out into the silver screen to unveil an epic Avengers tale, the untold tale left to be told is that there are equally epic twins tales of Justice on two Earths.