Fantastic Four, Avengers, and X-Men were also pretty pioneering in showing a superhero team in conflict, even if the Justice League did predate any of the big teams by a year or three.
I think it was really X-Men that nailed it. Fantastic Four -- well, Ben was the tragic character but I don't think there was really THAT much strife within the team; most of it was horseplay between him and Johnny, and that love triangle with Reed, Sue, and Namor. Avengers -- well, Hulk quit immediately because he's Hulk, but most everybody else got along, even after Hawkeye tied up the butler and shot arrows at him.
X-Men did a lot of the same light horseplay stuff too, but both Cyclops and Beast quit the team pretty early on. Only lasted one issue, but still.
Certainly Marvel nailed the Heroes with Problems stuff -- Hulk and Thing both struggling with their monstrous appearance, Iron Man constantly fearing his heart would stop, Cap coming back suffering from PTSD after losing his sidekick, and Peter Parker having pretty much any problem you could reasonably expect a guy to have and some you couldn't.
And the X-Men -- the allegory wasn't as pronounced as it became during Claremont's years, but it was there pretty early on; Beast quits the team because he's tired of protecting people only to have them turn around and call him "filthy mutie", and I believe the Sentinel/Master Mold arc was Kirby's swan song on the book.
X-Men was the book that really deepened the "strife within the team" idea under Claremont, and then The Authority and X-Statix each kinda took the premise to its logical extreme around the turn of the century. And pretty much every superhero team book (or toon) since has cribbed from them to some extent or other.
I'm skipping over a lot, of course, but those are all fairly important data points I should think.
Though speaking of Thor just being Norse myth, I do absolutely love that the comic was so popular they actually did do a spin-off that was just straight retellings of Norse myth. Tales of Asgard, I think. I have a TPB or two somewhere.
Yeah, that's where Thor really hit its stride; the Don Blake stuff wasn't as much fun as Stan-and-Jack Do Norse Mythology. (Correct me if I'm wrong, but that's the series where the Warriors Three debuted, right? Man I love the Warriors Three.)
Tangentially: Anybody ever read Horus? It was one of the Moore/Veitch 1963 books. It's pretty much what you'd expect from the context I'm bringing it up in: it's a pastiche of Thor, except instead of being a Silver Age superhero take on Norse mythology, it's a faux-Silver Age superhero take on Egyptian mythology. Really a great damn book.
Quick background:
1963 was a series Moore, Veitch, Bissette, and Totleben did in 1993, made up of tributes to Silver Age Marvel (and, to a lesser extent, DC) books. It was fun as hell, and it was never completed; it was all supposed to lead to a big team-up issue where all the characters traveled to 1993 and met the Image superheroes. Which should probably explain why it was never completed, because it's 20 years later and
the Image founders STILL can't finish a fucking project together.
Anyhow, 1963 is easy to find; it's a product of the 1990's boom, lots of copies got printed, and it frequently shows up in dollar bins.
Also, since Alan Moore has actively fucking sandbagged Veitch and Bissette's attempts to get the series reprinted, as far as I'm concerned it's okay to pirate it. Especially if you buy some new Veitch and Bissette books so they get some money in their pockets.
...wow, that's one hell of a tangent.
But still, yeah, 1963 is great, and Horus in particular is a thoroughly enjoyable takeoff of those Asgard stories.