Goku and Vegeta never had a truly equal race to see who was more powerful.
He was easily more powerful than Goku when he arrived on Earth, and even after King Kai's training, Goku was still vastly behind Vegeta in base power level, and needed Kaioken just to help him even it out for him.
Then Goku had the whole 100x gravity training while heading towards Namek, while Vegeta had nothing comparable to that.
When Vegeta first turned Super Saiyan however, he was a bit stronger than Goku was during the same time period as Super Saiyan, even before the Heart Disease started kicking in.
Then Goku got a big boost after healing up from that Heart Disease since it nearly claimed his life, so he was stronger than Vegeta when they both went into the Hyperbolic Time Chamber to train.
And then of course Goku eventually died, and reached Super Saiyan 3 while he was in the afterlife, where he could train for basically as long as he wished, and had tons of other strong opponents to spar with, while Vegeta is stuck on Earth able to do nothing but peace time training.
In completely equal circumstances--I'd give it to Vegeta.
And on Broly, you gotta realize that he never had to train a day in his life to get as strong as he was. He was naturally growing in strength at a rate Goku could not come close to matching despite intense training and fighting all throughout in the exact same amount of time, seeing as they are the same age.
