The fight between the two characters in the middle of the film, their actions in the battle of New York, and their attempts at beating Loki confirm that at least in the first Avenger film, the strongest member of Earth's Mightiest Heroes was Hulk. In Phases 3 and 4 of the MCU, there are characters that are vying for the title of strongest Avenger, such as Benedict Cumberbatch's Doctor Strange, and the role of the strongest Avenger is still up for grabs. The debate over who the strongest Avenger is in the MCU now includes a variety of newer characters, but it started with 2012's The Avenger and focused on Chris Hemsworth's character and Mark Ruffalo's character.
Even though both characters suffered the same fate after their fight on the Helicarrier, the same could not be said for the other, as he had to resort to Mjolnir to keep him at bay. Even though he lost his hammer in the movie, he was able to use his powers to save the people. The friendly rivalry between the two characters sparked discussions between audiences over who the stronger of the two is, which was further fueled by their brief altercation in the S.H.I.E.L.D. Helicarrier. After saying "I'm always angry" to Captain America, Hulk was able to change the trajectory of a Leviathan by himself to stop it from demolishing a building. Fortunately, both characters are confirmed to have at least one more appearance in the MCU, with the exception of She-Hulk. Only time will tell if audiences will ever get a true answer to the strongest Avenger debate, but as far as The Avenger goes, Hulk is Earth's Mightiest Hero. In the now-iconic scene of him smashing Loki into the floor and calling him a "puny God," Hulk didn't sweat.
Now that more characters are included in the discussion, the age-old question of who the strongest Avenger is will never be put to rest. The evidence shows that the Hulk was more powerful than the other Avenger, but that might not be the case today.
The outcome of their attempts at stopping Loki is the biggest indicator of the strength of the Hulk. This may not be the case in the current MCU, but in the film, it was proven that he is more powerful than Thor multiple times.
The strongest Avenger was decided by taking the powers each character displayed in the first Avenger into account. The journeys of two of the original Avengers could be coming to an end. His actions pale in comparison to those of the Hulk, who was able to block the portal with his lightning. The new weapon, Stormbreaker, gave him more powers, such as controlling the Bifrost. Bruce Banner merged his two identities, which made him less of a savage beast. In the battle of New York, Hulk's accomplishments were more impressive. Even with the help of Black Widow and Hawkeye, they are still evenly matched when it comes to stopping Loki.
Following their appearances in the 2012 superhero ensemble, the two characters have changed a lot. There was a reference to this in the film when the hero flew with a single punch.