Both Goku and Vegeta trained in the ROSAT(Room Of Spirit And Time)in preparation for the Cell games. Vegeta's day...or year, depending how you choose to look at it...took him above and beyond Goku. However once Goku entered the ROSAT, he managed to perfect his SSJ for to the point that it's natural for him with no strain, making him dramatically stronger than Vegeta. Yes, Vegeta entered the ROSAT for a second day, but look at his reaction when Goku powered up to full against Cell. Vegeta is both amazed and afraid.
...so yeh, Goku greatly surpassed Vegeta in both strength and speed. Something you'll find out by seeing more DBZ is that Vegeta only ever does well in battle when he's stronger/faster than his opponent. Vegeta is so outclassed by Goku at this point that individual fighting styles wouldn't even make much of a difference at all. The gap is too big.
Goku wins this one easily.