Fans know quite well that the author of the series Akira Toriyama initially loved Goku and disliked Vegeta. But as the story progressed, the author came to like Vegeta more. And Akira Toriyama gave the Saiyan Prince a major advantage over his rival, something that Goku fans couldn't help but accept.
The Key Difference That Makes Vegeta a More Skilled Fighter Than Goku
While Goku is a genius fighter, it is a well-known fact that his moves are often passed down from his friends and family, starting with his grandfather Gohan and Roshi. He has almost no techniques that can be called his own (maybe Dragon Fist, but that is not canon).
Vegeta, on the other hand, has most of his own self-developed techniques, including Galick Gun, Final Flash, Big Bang Attack, Final Shine, Photon Bomber, and Gamma Burst Flash. While most of them are just variations of Ki Blast, at least the Saiyan prince tried to create them, unlike Goku.
Even in Dragon Ball Super, Goku copied from Beerus and used Hakai to stop Fused Zamasu as a last resort. While Vegeta could learn to use the Teleportation technique, he did not do so out of pride, not wanting to copy Goku's signature move.
Even though Whis informed Goku and Vegeta that they needed to know how to use Ultra Instinct, during the Tournament of Power, Vegeta realized that Ultra Instinct was not for him and wanted to take a different path. Therefore, he asked Beerus for help and was inspired to activate Ultra Ego for the first time against Granolah.
Vegeta is one level below Goku because of a fundamental flaw
Vegeta was imbued with the ideals of Saiyan Pride from his father from a young age. However, Dragon Ball Super: Broly director Tatsuya Nagamine stated in a January 2019 interview that the Saiyans lost their original pride as a warrior race when King Cold and Frieza invaded them.
The proof is that King Vegeta never challenged Frieza or did anything similar against the invader. Instead, he just bowed down to Frieza and used deceitful tactics against his subordinates. This means that King Vegeta himself had no idea what the Pride of the Saiyans truly meant.
At that time, Bardock was perhaps the only Saiyan warrior who kept the pride of the warrior race.
Broly, Goku, and Vegeta left Planet Vegeta as children. Only Vegeta lived on his home planet for a while, and because of his childhood memories, he has the false pride of a prince.
During the Granolah arc of Dragon Ball Super, both Goku and Vegeta truly learned what Saiyan Pride really is through the story of Bardock. It was Vegeta's false pride that affected his progress. Now that he understands what it is, he can properly break his limits in the future.