Originally Posted by
Revolutionary_Jack
The Fantastic Four as a comic introduced and built the Marvel Universe...the Skrulls and the Kree, the Inhumans, Wakanda, Annihilus and the Negative Zone, Doctor Doom were all introduced in its pages. Likewise Namor of Atlantis was reinserted into Marvel Continuity in its page, and that set the stage for fellow Golden Ager like Cap to be thawed out of ice later.
So the overlap has always been the Fantastic Four and the rest of the Marvel Universe and not with the Avengers per se. The Avengers don't really have a team identity and core theme unlike the F4 and the X-Men, so because they don't have a thematic idea it becomes "a newspaper of the MU" kind of theme, so that's why people see that overlap.
It's true that there's never really been a big crossover event centered entirely on the Fantastic Four...Secret Wars 2015 is probably as close as it gets. But even EMPYRE is promoted jointly as a Fantastic Four and Avengers team-up, so while there's overlap there's also an acknowledgement of spheres of influence.
To be honest, it's probably time for a Avengers v. F4 crossover story to set boundaries between the two to distinguish between them.
Talking about Cap isn't the same as talking about Avengers. People can like Cap and not necessarily like the Avengers. Look at all the people who joined "Team Cap" in CIVIL WAR.
The favorite hero of the former for quite a while has been Frank Castle, the Punisher...he has supplanted Cap for them.
Within the 616 Marvel Universe, Cap has had ups and downs. He went "Nomad" after taking down Nixon (although obviously it's no longer him as it was originally in Englehart's run). He went against the US Military in Daredevil Born Again, he was in-universe unpopular in CIVIL WAR (even if out-universe he was obviously in the right, by virtue of Team Iron Man creating N-Zone gulags with the aid of "useful idiot" Reed Richards), and obviously there's been a stigma to him as a result of "Hydra Cap". Within the mutant community (and also X-Men fans), Cap has always had tension because he represents American ideals but never speaks against the fact that his government has put into effect and enforced genocidal and racist policies against mutants. This dates as far back as SECRET WARS '84 Now as a reader you give a pass because obviously that's a case of the fact that the shared universe goes only so far...and Steve's fluctuating unpopularity actually makes this work in his favor.
Steve Rogers is genuinely loved more than Tony and Thor are inside the 616 MU. Thor is respected and admired but he's also distant, remote and generally not on Earth so often. Tony Stark is admired for his brains and considered cool...but people who think someone's cool don't necessarily love those people. And Tony also has his critics, a lot of them justifiable, and obviously as a rich dude there are people who will dislike him for general principle (as they should).