Even though Goku and Vegeta fought together for the good cause plenty of times, the Saiyan Prince has always been envying his long-time rival for being stronger. Even if Vegeta dedicated his life for surpassing the one he always calls ‘Kakarot’, his wish was already granted only several times in the franchise. The problem is that the surpassing didn’t last for too long, and Goku is still one step ahead most of the time.
Vegeta is still a smarter character than Goku, and we have to give that to the Saiyan Prince. The advantage that Goku seems to have is that he ‘was born with a natural talent far beyond’ the one of Vegeta, as the Prince of all Saiyans himself admits.
Having a tail just like Goku had as a kid, Vegeta could also transform into a Great Ape (aka Oozaru) as he looked at the Moon. But Vegeta was a bit more clever, as he tricked his brain into thinking that an energy wave floating on air is actually the Earth’s natural satellite. Thus, Vegeta could transform into Oozaru and surpass Goku’s strength tremendously. Vegeta was then literally crushing Goku’s bones, although the Saiyan Prince was significantly dominated in battle by his opponent until that point. This is the first battle between the two Saiyans in Dragon Ball Z, and Vegeta was at that point a completely evil character.
Training in the Hyperbolic Time Chamber
Vegeta became significantly stronger than Goku after training in the Hyperbolic Time Chamber with Trunks, the son of the Saiyan Prince who came from the future to warn everybody about the androids. For a short time, Vegeta surpassed Goku once again, and he proved it by mopping the floor with Cell during his incomplete form. But Goku also entered the Hyperbolic Time Chamber himself along with his son Gohan, and they both surpassed Vegeta in the end.
Seeing Bulma slapped by Beerus
During the first arc of the Dragon Ball Super anime, the God of Destruction Beerus was threatening to destroy the Earth. Oddly enough, Beerus wasn’t exactly an evil character. He was willing for such an awful deed for having to maintain some sort of balance in the Universe. Goku was easily defeated by Beerus with two blows, even during his Super Saiyan 3 transformation. But for several seconds, Vegeta managed to develop a power way higher than a Super Saiyan 3 and teach some manners into the God of Destruction the hard way. Beerus made the huge mistake of slapping Bulma, and that’s what triggered the enormous power boost and unquenchable anger in Vegeta. Master Roshi also emphasized that Vegeta surpassed Goku at that point. Even if it was for a very short while, it still counts, and it proved to everyone that the proud Saiyan Prince loves his wife madly.
Vegeta was way stronger before the two Saiyans ever met
Vegeta was light-years stronger than Goku when the two warriors were teenagers and kids. Vegeta was introduced at the beginning of Dragon Ball Z, and he was known as a space pirate who killed entire alien races at the orders of Frieza. Goku could barely be a worthy opponent against his evil brother Raditz, and our hero died in that battle. When he was severely injured and about to die, Raditz held a final speech saying that fighters far stronger than him will arrive to Earth in one year and ready to avenge his death. He was referring to Vegeta and Nappa. Therefore, Vegeta was far stronger than Goku in Dragon Ball Z before the two Saiyans met during their first epic battle on Earth.
The problem is surely not that Vegeta never surpassed Goku. The problem is that Vegeta wants to do it for good. But at this point, Vegeta may still be able to defeat Goku during a one-on-one battle if things are not taken too seriously by both of the two mighty Saiyans.