Continuing on the relations between Earth-777's most renowned super-teams...
Appearances aside, it isn't as if the Avengers and the Justice League didn't respect each other; everyone on both teams respected Cap (Steven Rogers) and Superman. Even Batman begrudingly admired Captain America's leadership and tactical skills (his physical prowess was dismissed as "a chemical byproduct"). It rankled Batman that the "rules" agreed to by each during "official" team-ups put CA in charge of field ops. But deep inside, the Dark Knight knew this was the right decision. Thor genuinely liked Superman, the more than mortal who devoted his life to Midgard. The Thunder God was slightly disappointed in Kal-El's lack of battle skills and naive attitude, but figured the youth would improve in a few hundred years. The Prince of Asgard also has an eye for Wonder Woman, even though a brawling Norseman was not her cup of tea. WW always found Simon Williams charming in a clueless, bumbling way, though she sometimes teased him a bit much. He never really caught on.
The Flash got along with everyone (except Quicksilver, enough of a jerk to carry on a one-sided rivalry). Hawkman and Hawkwoman were fast friends with with Hawkeye (maybe just to irk GA), Thor, and especially Ms. Marvel. The Vision almost "adopted" the more hapless Red Tornado as a kid brother, helping RT realize early on that Kathy Sutton and Traya didn't need a human being in their lives, just a good man. RT repaid the favor when his more advanced diagnostic systems found the "stealthware" Ultron had implanted in the Vision. (Ultron got a little visit from the two-along with the Metal Men, Aaron Stack, Jocasta, and others from the "inorganic community'-Ultie got the message). Zatanna befriended the Scarlet Witch, tutoring her in real magic, introducing her to pureblood Homo Magi such as Agatha Harkness, and helping thwart a mystical kidnapping of Wanda and the Vision's boys.
Earth-777 faced numerous threats thad demanded the two groups combine forces. During Galactus' first assault on Earth, the JLA along with Iron Man and Thor kept numerous threats launched from Galactus' World-Ship from reaching planetfall; the ground bound team members faced the Devourer's "Punisher" cadres to give the Fantastic Four and Doom Patrol time to bring an end to the menace.
The first Skrull invasion of the planet was exposed when Batman tipped off the Avengers about his deductions ("I don't really like your team...but the public only needs to fear one hero. That would be me.) The Skrull's plans fell apart with their infiltraion of media and politics exposed. Then Superman, J'onn, and the GL Corps (led by Hal, of course) tied up the Kree armada while the Avengers dealt with the Skrull fleet.
Later, when the Sinestro Corps hit Earth, the GL Corps and the JL were paid back in full for their previous assistance. Prime found out magic hammers DO NOT "tickle"-when they're backed by a Norse God wearing his Belt of Strength; Captain Marvel (Monica Rambeau) was zipping about all over the battlefield, soaking up the juice from the Sinestro rings and then putting Prime down for the count with a blast of red solar radiation. Cyborg-Superman found out what every other tech-villain over the years has learned: don't mess with Tony Stark. Sadly for Sinestro, fear was just nowhere to be found that fateful day.
But still...there have always been too many personality clashes for the teams to really be friends. Captain America couldn't understand why a man of Batman's gifts wanted to frighten and bully people, rather than inspire them.Hercules never forgot the beat-down he received from Superman when the Olympian decided to share "The Gift"-he had never been so humbled by a mortal.Diana always saw right through Hank Pym in any guise-a good but weak and insecure man.
The young T'Challa was intermittently involved with Nubia, the "African Wonder Woman", for whom Diana had no love lost. Some of the more cosmopolitan Avengers (all New Yorkers) thought snidely of Barry Allen, Ralph Dibney, and Ray Palmer as small town rubes. Batman never got over being suspicious of ex-thief Hawkeye and ex-KGB agent Black Widow. Gotham's Finest almost went into a cold rage when the Avengers allowed "that unimaginative, jumped-up thug" Moon Knight into their ranks. Hal Jordan tried to bark orders at Avengers the way he knew r he couldn't do with the other Justice Leaguers. Tony pegged GL as a guy who would be just an employee at Stark Industries.
And Quicksilver was still a jerk.
The Contingent: When all other super teams fail...