Both have incomparable strength, but I have to go with Goku

Vegeta first appeared in the Vegeta Saga, and was way stronger then Goku then. But when Vegeta and Nappa came to Earth for the Dragon Balls, Goku beat Nappa with ease because of his training with King Kai. When he fought with Vegeta, Goku ended up winning because Vegeta retreated after getting beat up by Goku along with Gohan and Krillin. When Goku went Super Saiyan for the first time, his strength went past Vegeta's and Goku easily beat Frieza. However, Vegeta went Super Saiyan in the Androids Saga and exceeded Goku by a little. In the Majin Buu saga, Goku reached Super Saiyan 2, so did Vegeta. When they both fought, it was a tie. When Goku went Super Saiyan 3, he exceeded Vegeta by a long shot.

Goku and Vegeta are now at Super Saiyan 4, but Goku could exceed Vegeta by a little because of his forms being quite more Powerful then Vegeta's. Therefore, I think Goku would win if these two Saiyans had a long and Bloody fight.

Vegeta gets killed way to easily from me, and Goku is pretty strong.

@rileyferguson: Indeed. :D (I'm STALKING you once again)

Emy-chan, you never give up. STAHP!!! XD