Goku would win in a battle over Vegta. In fact, he has done so many times and actually Vegta admitted defeat to Goku in one version of the game when he offers to team up with Goku to take on Buu. Goku just has more power and versatility when it comes to fighting with Vegta.
Yes, Goku would win in any conflict with Vegeta, anywhere. In fact, over the course of Dragon Ball Z, he handily defeats Vegeta no less than four times. Vegeta finally admits defeat to the superior warrior when he offers to merge with Goku so that the two can take down the powerful Buu.