None of the rivalries and feuds across the perennially popular Dragon Ball franchise are perhaps more iconic than the longstanding competition between Goku and Vegeta. Dating back to the beginnings of the manga/anime series Dragon Ball Z, the two Saiyans have constantly attempted to one-up each other to become the strongest in the Dragon Ball Multiverse.
While this contest of strength has ebbed and flowed with physical comparison, the question remains which of the two longtime frenemies is the smarter of the duo? With Vegeta something of a master tactician and Goku holding surprising insight on the more ephemeral ways of the world, arguments could be made for either one. However, what edges Goku ahead: wisdom.
Goku being something a simple country boy has been a running joke for much of the franchise. Raised in isolation at Mount Paozu by his adoptive grandfather Gohan until the age of 11, Goku remains naive to the ways of the world, unfamiliar with concepts such as kissing and holding down a regular job while humorously failing his attempts to earn a driver's license. Vegeta is the polar opposite, born and raised as Saiyan royalty, working his way into Frieza's favor after the villain secretly destroyed the Saiyan homeworld. An elite within the Frieza Force, Vegeta grew up hardened and constantly immersed in combat and conquest.
Goku and Vegeta's martial arts teacher Whis, in the sequel anime series Dragon Ball Super, perhaps summarizes the differences between the two Saiyans the best. During a sparring session with the two attacking him simultaneously, Whis observed that Vegeta was a tactical genius who constantly was planning what his next move would be in the heat of battle. This, however, kept Vegeta from letting go into the free flow of combat and prevented him from attaining the Ultra Instinct transformation. With Vegeta unable mentally to get out from his own way, Goku has an edge as a more naturally intuitive fighter, allowing him to achieve the powerful transformation.
Since his decidedly antagonistic introduction, Vegeta has come a long way but still has a lot to learn from Goku's omnipresent serenity and removal of self from his worldview. Conversely, Goku's more apparent naivete on the world's ways will continue to be a running joke and defining trait of the character -- a compassionate warrior who only understands combat and is largely uninterested with the rest of the world. Goku and Vegeta are excellent at what they do in their respective ways, which extends to their mentality and outlook.
This contrast between Vegeta's intelligence and Goku's wisdom is apparent from more than just the two warriors' respective fighting styles. Vegeta is constantly hounded by the inner demon of living up to his Saiyan birthright to become the mightiest warrior in his race; that means his hubris often gets in the way -- as exemplified by allowing Cell to become perfect -- and obsessed with surpassing rivals like Goku.
Goku is generally more engaged with finding a worthy challenge. He certainly wants to become the best fighter he can be but has no qualms admitting Cell is stronger than him or having his son Gohan replace him to become the world's strongest hero. This level of serenity is shown how often Goku is willing to sacrifice himself in battle; Vegeta's only sacrifice came with the Saiyan Prince still comparing himself to Goku as he fought in vain against Majin Buu.