Why does Goku always know how to train more "effectively" than Vegeta to stay ahead of him even if Vegeta trains harder?

It’s not exactly accurate to say that Goku knows how to train more effectively. You have to understand that there are differing circumstances behind Goku and Vegeta’s training methods.

Goku has always had Masters to learn from. He’s never just relied on his own power and instincts. He’s always been open to guidance. First, it was Grandpa Gohan, who taught him the basics of Martial Arts.

Then, it was Roshi, who gave him further knowledge of martial arts and helped him to understand the value of resting your body.

Next was Korin, who helped him to eliminate superfluous movement.

Then, Kami, who taug

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Because….

Unlike Vegeta, Goku has had many masters who have taught him different things individually.

Grandpa Gohan taught him the very basics of Martial Arts and combat.

These fights are like the weather. No guarantees.

—Grandpa Gohan

Master Roshi taught him Martial Arts on a higher level, how to increase his strength, and how vital it is to rest as much as it is to train.

Move well, study well, play well, eat well, and rest well.That is the Turtle Master way!

—Master Roshi

A little fun fact:- Do y’all know “Roshi” and “Kame Senin Ryu” are both just titles? We actually don’t know his real name.

Master Korin pointed out his wasted movements during combat and taught him how he can be more efficient in battle.

See, you should move like you speak. With purpose and clear direction.

—Master Korin

Mr Popo and Kami taught him to command his energy and be calm during battle.

Be as calm and tranquil as the heavens

—Mr popo

King Kai taught Goku to not just train his body, but also his inner life force or energy itself

Train not just your body, but also your spirit

—King Kai

Compare that to Vegeta whose only true teacher/master to this day is Whis, and perhaps Beerus later on.

Goku has learned of many things that Vegeta never did, which always kept him one step behind Goku throughout all of DBZ and even the majority of Super. Vegeta is indeed a strategist with a high battle IQ on par with Goku, but unlike Goku, Vegeta was already born strong and only ever trained to kill and bring destruction rather than to discover himself like Goku did.

Vegeta clouded himself with arrogance and accumulated experience by wiping out civilisations throughout the cosmos. That made him a formidable warrior. Goku on the other hand humbled himself and allowed others to pass down their knowledge and experiences to him. And that’s how Goku became a formidable warrior. There’s a difference between what kind of individuals they truly were the majority of their lives. And it ultimately impacts their combat mastery.

Even though Goku’s teachers were “weak” compared to Vegeta, strength isn’t everything. And he realised this eventually.

The wisdom of these “weak” individuals passed down to Goku is what kept Vegeta unable to ever catch up. And it is also what led to Vegeta admitting Goku is indeed Number 1.