Vegeta's real issue was the fact that he, a Saiyan elite and prince, got his ass thrown around at all by a lower class Saiyan like Goku during their first fight. Their first battle was in Vegeta's victory since Goku couldn't win without Gohan, Krillin, and Yajirobe's help, and the second match was forfeit because they both decided to focus on Buu (although Goku could have won had he fought seriously)
That was never the issue though? If one actually followed the series from the start, then it should be noted that Goku HAS NEVER won against Vegeta in a straight fight.
