There are tons of heroes in shonen anime who everyone around them aspires to match. They stand as pinnacles of power and might, thanks to either years of training or gifts of strength. Among these higher echelons of power, two stand apart as among the mightiest in their respective series: Son Goku from Dragon Ball Z and All Might from My Hero Academia.
Everyone aspires to match or surpass them. However, which of the two is mightier? Which of the two is stronger, and which embodies all that a person should aspire to be?
Who is Stronger?
To ask who has more raw strength is an unfair question. The answer is undoubtedly Goku.
All Might has never come close to matching Goku's levels of raw strength at any point in My Hero Academia. Sure, his punches can cause the planet to shake, but never has All Might demonstrated the sort of powers Goku has. Ignoring how Goku's fight against Beerus in Dragon Ball Super nearly ruptured holes in reality itself, Goku had enough power as a child to destroy a small moon. All Might is no planet buster.
Furthermore, Goku's weakness, his tail, stopped being a problem once he cut it off. By contrast, All Might's weakness is the injury left upon him by All-For-One, an injury that has weakened him ever since he received it. Goku can fight for hours and hours, while All Might needs to push himself to even fight for more than a few minutes. However, even if All Might stood against Goku at his prime, he'd still fall short of the Saiyan's power.
But there is more to being a paradigm of power than just being strong.
Who is Mightier in Their World?
Both are arguably the strongest characters in their shows, but only All Might stands as the mightiest from start to finish. Both characters start from a place of disadvantage. All Might starts as quirkless Yagi Toshinori, a boy who just wants to do good for his world. Goku starts as the son of a Saiyan grunt, Bardock, who loses all his memory after some head trauma.
However, Goku, while he does save the world and universe time and time again, has to train for his power. All Might is deemed worthy, learns how to harness his abilities, and, after working hard, becomes the best. But it doesn't hurt how he is granted phenomenal power from the get go. Goku had to earn all that power on his own. All Might needs to credit his mentor, Nana Shimura, in part for his greatness.
However, that said, All Might is by far the strongest hero on the planet. He is the best of the best. Even his ultimate rival, All-For-One, is beaten more than once by All Might. All Might's presence as the pinnacle of strength actually affects the political landscape and boundaries between heroes and villains. His retirement leaves a power vacuum in its wake.
Nothing really changes when Goku dies. Other characters rise to take on the Saiyan's role. Goku isn't even the strongest character in the series. After all, whenever Goku reaches a new level of power, there's always someone ahead of him waiting. Goku beats Vegeta? There's Frieza. He beats Frieza? Androids. Then Cell. Then Buu. Then Beerus. There is always someone bigger Goku, now at a new pinnacle of strength, has to face off against.
Moral Inspiration
Goku is not a very good person. Goku selfishly obsesses over improving his own power for its own sake. He fights for no greater goal than his own perfection. Sure, when the universe is at stake, he will fight to protect it, but his primary motivation is always to find a challenge he will need to overcome.
It's telling that all his allies, many of whom are former adversaries of his, have a stronger moral center than Goku ever can, including former rival and villain Vegeta, who by all accounts is a more involved father and husband.
By contrast, All Might is a hero. He exists as the moral goal that inspires confidence and hope in all those he meets, even at his own expense. Despite his injuries, he continues to be a smiling hero to inspire goodness in others. His heroic actions over the course of the series worsen his physical condition, yet he goes out to be a hero regardless. He isn't self-serving. He isn't self-centered. All Might simply knows that, if he doesn't stand for something, people will suffer.
Even more telling is how the two help their proteges. Goku is an awful teacher who, despite seeing greatness in Gohan, never realizes the great risks in pushing Gohan into combat. Goku never considers what Gohan wants. Compare that to All Might and Midoriya. All Might comes to love Midoriya like a son after seeing Midoriya's resolve to save others.
Is Might Only Power?
In articles like this, it is tempting to say that the person who would win a fight is truly mightier. If your interest is to see who could beat the other person to a pulp more, Goku wins. There's almost no competition.
However, if your question is who stands as a greater hero, it's All Might, who truly embodies what it means to be number one and inspires those who see him. All Might is the superior, mightier hero, even if he'd never stand a chance against Goku in a real fight. After all, All Might would keep fighting even as his body gives up on him. Plus, it's hard to imagine Goku not respecting the resolve to win under All Might's conditions.