During the seven years Goku was dead, Vegeta according to his own words trained non-stop to catch up to Gohan. Then came the whole World Tournament thing and Goku said he was gonna take a 24h leave from the Otherworld in order to participate in the Tournament.
Now. Vegeta knew he was far more powerful than Gohan. Mostly because he had been training non-stop while Gohan stopped training altogether after the Cell arc.
At the time Vegeta still felt that huge rivalry towards Goku. I believe he actually believe he had finally surpassed Goku.
Then comes Babidi and they have to go through those levels of the ship. The first level guardian was a weakling even Goten and Trunks could’ve beaten with both hands behind their backs.
The second guardian however. Yakon if my memory serves me well had this ability that allowed him to devour Ki from his opponents, especially Ki that was being so loosely released, which is the case with all SuperSaiyan forms. So while in SuperSaiyan 1 Yakon has no problem handling Goku’s Ki. But then Goku gives Yakon and Vegeta quite the surprise he for one single second goes SSJ2. Yakon is blow apart but in that one second Vegeta was able to see that Goku in SSJ2 was stronger than him.
So he laid the bait so Babidi would try to possess his mind and grant him extra power. Just like Babidi had done to those two humans that had participated in the World Tournament. You saw how he took two weaklings and gave them Ki abilities. So Vegeta wanted so desperately to surpass Goku that he actually resorted to borrow power from Babidi.
Also part of Vegeta believed that it had been his new more calmer nature that had made him be always one step behind Goku.
So Vegeta becomes Majin Vegeta, goes into a boosted SSJ2 that we knew was not natural mainly because of the red sparks Vegeta aura had instead of the normal white sparks.
But important details were revealed in the fight between the two. First and foremost we got to know that Goku for those seven years he hadn’t trained non-stop. In fact when Vegeta tells him he had, Goku seems actually surprised, and says he hadn’t trained for a while and only began training again more actively because of the Tournament. Meaning Goku trained for what… Two weeks at most? Regardless we see that for the most part Goku and Majin Vegeta were tied and obviously while Vegeta was fighting to crush Goku, Goku had no intention of doing that to Vegeta. If he had then all he would’ve needed to do would’ve been to go SSJ3 for like one second or two and he would’ve finished off Vegeta.
In a manner of fact when Goku wants to fuse with Vegeta he initially refuses really because he was pissed off at Goku because according to Vegeta he had gone soft on him, by not using the SSJ3 form against him. Which of course when Goku said he only used that form for emergencies that didn’t made it any better, seeing he was indirectly saying that even with the power Vegeta had gained from Babidi Goku still didn’t considered Vegeta to be a threat to him.
But funny enough when Goku points out that he had only began training again the last two weeks before the Tournament, Vegeta says to Goku that he had realized a long time ago that Goku capacity for training and fighting was unmatched. And no matter what he did Goku would always be one step ahead of him. But while he accepted that a part of him also didn’t accepted it. He couldn’t understand how he the “Prince of the Saiyans” was always behind someone that wouldn’t even had made it into the Elite Saiyans.
In DBS we finally see Vegeta come to terms with the fact that Goku is simply more gifted. He doesn’t know why or how Goku does it, but he has finally made peace with the fact that for him, he’ll have to start finding his own paths to power and not race behind Goku.