Goku wins, but he gets help from Yajirobe who cuts Vegeta's tail off which makes him become normal again.
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They are both strong, but if you want to know who is stronger, they acutally fought. The fight ended in a draw. A few episodes later, when Vegeta realized Goku could have turned into SSJ3 and beat him down, he got mad at Goku for having held back. So the answer is, Goku was tremendously stronger at the time although he withheld his power to give Vegeta a fair fight.
because goku was n space at the time so baby went for the strongest one there. (vegeta)
Episode 214: Vegeta's Pride. Goku turns to USSJ (Ultra Super Saiyan) and USSJ2 in the Hyperbolic Time Chamber. He turns to SSJ2 while fighting Majin Vegeta.
Goku becomes super saiyan 2 when he is training in a special room at Kami's lookout. It allows a year to pass in the room, while real time in the outside world is just a day. He acheived SS2(Super Saiyan 2) right before he battled cell. So did his son Gohan. Even though Goku was stronger than ever at that time, Gohan was stronger than Goku, achieving SS1 and SS2 in the special room. Gohan was the first one to go SSJ2. Goku became an Ultimate SSJ in the Hyperbolic Time Chamber. Goku went SSJ2 for the first to battle Majin Vegeta, which was about 7 years later. Gohan went SSJ for the first time in the Time Chamber, and SSJ for his fight with Cell.
In episode 153 (episode 168 in the original, non-dubbed episode) of Dragonball Z, Gohan and Goku emerge from the hyperbolic time chamber. After Goku and Gohan leave the time chamber Piccolo, Vegeta and Trunks then use the chamber for themselves.