If we exclude every unfair power-ups Goku and Vegeta had, Goku only came up with a better idea for training in ROSAT once, and Vegeta instantly figured Goku's training plan after seeing him. By training alone in ROSAT for 1 year Vegeta surpassed half of Goku's power.
You like to emphasize on the "once" part because this would make Goku's "brilliant" training method (that Vegeta comented on again and again, both in the Buu Saga AND in the Cell Saga) seem like an accident , a one time deal. Sorry, but no. The author made the difference clear once by showing the difference in the results between them when they start training under the same conditions. I don't think he needed to come up with another situation to prove the same thing.
What's more, he figured out what Goku had done but still couldn't reach the same results. It doesn't matter that he trained alone the second time since he also trained alone to reach SSJ 1.
In Boo arc Vegeta, who had trained harder but under worse conditions than Goku did, was pretty close to Goku in power. He was confident that Babidi's spell would give him enough power to close the gap between them, without knowing how much power Babidi can grant him.
I don't think he was pretty close to Goku in power because otherwise he wouldn't have become so desperate to turn to Babidi. It only took a couple of moments of watching Goku in action for him to realized Goku was stronger and I don't think he would have done something so drastic like helping Babidi if the difference was small.
On Earth, I doubt Goku has gravity room to train in, so Vegeta has an advantage of that. Goku can teleport to the afterlife, though.
Yes he can, but does he? We know Vegeta has his gravity room, we do not what Goku does to train.
And I don't think that Goku was that much stronger (if at all) than Vegeta at the 28th Budokai.
If he was, than why didn't Goku look forward to fighting Vegeta in that tournament. It's been clearly established that Goku had been bored these past years and the real reason he started training Uub wasn't to have a succesor as Earth's defender, but to finally have another opponent. Something that Vegeta obviously hadn't managed to become by that time.
In the alternative ending of DB Toriyama drew for a special edition of the manga, he even shows Vegeta saying "one day I find a way to surpass you" meaning that in-universe and in the authors mind Vegeta was still weaker than Goku.