Um, no. That's the obvious, real-world-view interpretation, but the in-verse validity of that comparison came to a screeching halt, barely more than a year into their existence, with Cap's Kooky Quartet. The JL has almost always been looked upon in-verse as some mixture of The Round Table and The Olympic Pantheon (minus all the icky spite and rape stuff). Pretty much from Avengers 1.17 on, the Avengers have been eyed with at least a bit of sketch by the citizens of their world.
The FF have had their own share of troubles, but neither to the scale nor with the consistency of those Earth's Mightiest have endured.
The problem with Justice League and Avengers comparisons/mashups is that the two universes are wired differently, and the meaning and status of the title in one does not correspond directly to something similar elsewhere.
In a superhero story, it's not enough for the writer/editor and so on to declare pre-emptively, canonically, that so-and-so is the greatest or so-and-so has this status and call it a wrap. That's not how this works.
In DC, the characters have an in-universe status not because of writer/editorial edict but because of actual historical fan acclamation. The in-universe status reflects the status the characters had in the real world. The reason Superman is considered the greatest hero in the DC universe is that he was actually the first and for a while the biggest and most famous superhero character, certainly in the 50s. Batman is a street level hero like Spider-Man (nominally at least) but because he was DC's second biggest hero he also became Superman's best friend and equal even if in story terms it didn't make sense given that Superman could clean up Gotham in a day or two if he put his mind to it. When the Justice League was formed -- a team with Superman, Batman, Wonder Woman, The Flash, Green Lantern, and so on (obviously roster's changed and gone back and forth, don't @me) all those characters had a presence and success in popular culture out of universe in real-life, that added gravitas to the in-universe team-up between them. When DC sold Justice League as the ultimate crossover and best team ever, in its time, they didn't need to convince people since by default it was true.
Whereas in the Marvel Universe, they put the cart before the horse. The Fantastic Four were configured from the get-go, before the fans had a say in it, to be the greatest team in the Universe. That meant that the in-universe status of the characters never entirely synched with the way the characters had about them outside. The Fantastic Four of course in the '60s was the biggest Marvel title and their most popular for a while but that's not been the case after the '60s.
In the case of the Avengers, the Big Three of the Avengers -- Iron Man, Captain America, Thor -- have never represented, in the eyes of Marvel fans to have the same stature as Batman, Superman, and Wonder Woman. Don't @me about the in-universe status, that's irrelevant here. Don't @me about the movies, also irrelevant here. We are talking about 616 Marvel and the Avengers have never consistently been or held on to being Marvel's biggest team. Ultimately, it's how the fans respond to and feel about these characters. In terms of fan acclamation, Spider-Man is Marvel's Superman and Batman. He's the only character fans feel strong enough on a level comparable to Superman in the '50s or Batman since the mid-70s. Marvel's biggest team is historically the X-Men, that's who fans chose to be Marvel's biggest team.
I mean, in terms of in-universe standing and how the general public in-universe view them I don't really see that much of a difference between the two since they're both the main Superhero response team for most major threats on the Earth and above.
I always thought among Heroes the Avengers were more respected. I am always hearing someone say what an honor it is to be invited to join. At least in the 60's and 70's But I havnt heard to many heroes talk about how great it would be to be on The Fantastic Four.
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I would say the reason why the FF aren't as respected as superheroes is because, technically, they aren't meant to be superheroes as much as they are explorers. They just happen to fight crime as well.
With the Avengers, they were outright formed to be a superhero team.
Reed and the rest of the FF might get more respect for their contributions to science than any heroics they did. Of course, this is mostly a semantics argument, so take it with a grain of salt.
"We live in a world of cowards. We live in a world full of small minds who are afraid. We are ruled by those who refuse to risk anything of their own. Who guard their over bloated paucities of power with money. With false reasoning. With measured hesitance. With prideful, recalcitrant inaction. With hateful invective. With weapons. F@#K these selfish fools and their prevailing world order." Tony Stark
Also you're unliolkely to get the whole "honour to join" thing with the FF because they're a family first. That makes others joining rarer than with the Avengers and that kind of talk wouldn't feel right. It's a different dynamic where it's more like being a family friend so talk of honour and stuff would feel off.
Be sure to check out the Invisible Woman appreciation thread!