Contrary to what the title might imply, Ultimate Spider-Man focuses on the life of the original webhead, Peter Parker. A basic 616-template of the character undergoing SHIELD training so that he might one day become The Ultimate Spider-Man. Over the course of his series, Spider-Man's adventures lead him to cross paths with all facets of Marvel lore. For a start, Peter isn't the only one undergoing SHIELD hero training. He's joined by teen versions of White Tiger, Power Man, Iron Fist, and Nova (Sam Alexander). Beyond the diversity of his own team, missions and mishaps lead him into deep space, wars with the undead, and hellish other realms alongside the likes of the Guardians of the Galaxy, Blade, and Dr. Strange. Eventually, Pete is even dragged across the multiverse and ends up bringing fan-favorite Miles Morales back along for the ride.
Despite being the second show in the 12041 cannon, the story of Avengers Assemble pre-dates Ultimate Spider-Man by several years. Tony Stark and the Avengers are household names even during Pete's earliest days as Spider-Man. An expansive history, and a complete roster of fully realized heroes (+1 rookie), allow Avengers Assemble to branch out even further into its mythos. Loki, Ultron, Infinity Stones (and the Mad Titan who covets them), The World Eater: Galactus, and the Beyonder. The Avengers face all of these challenges and more.
When not saving the universe with the Avengers, Hulk can usually be found saving it with the Agents of S.M.A.S.H. A team of gamma heroes determined to change public perception of "Hulks". The team consists of Big Green himself, A-Bomb, She-Hulk, Devil Dinosaur (the bestest boy), and General Thadeus "Thunderbolt / Red Hulk" Ross. While Hulk tries to keep this team lowkey for the sake of public safety (and public relations), AoS tends to find itself pulled into Earth-rending threats fairly often. Galactus, Ego, and the inter-stellar grand champ Xemnu have all threatened the Earth's very existence, and all have been repelled by the Agents of S.M.A.S.H. A turn of bad luck even put them face-to-face with the Spirit of Vengence, and all Hulks lived to tell the tale.