Ok, people request that sort of stuff so I will share my thoughts about Goku, Vegeta and what was shown in 9 chapters od DBS manga.
Goku vs Vegeta was a subject covered by more dbz addicted people than I am (yes, there are few people like that, but in Poland it's most unlikely) and I agree with most things they are saying. But let's look back to the first time Vegeta battles Goku.
Their first battle was totally dominated by Vegeta, a Saiyan elite veteran warrior, who spent his entire life on pushing his body to further limits and who battled many wars, conquered many planets and was basically a prodigy fighter.
Goku on the other hand was a weakling saiyan, sent to Earth where he received a training from the best possible martial artists, gods included (Kami, King Kai and whatever being is Lord Popo). Goku states in a battle with Vegeta "even a weakling can surpass an elite if he trains hard enough" which of course is true.
Here the first major factor in their comparison are the mindset and reason to fight. At first sight Vegeta trains and fights to win, to get stronger, for his personal gain. Goku on the other hand fights because he enjoys it, fights to defend the Earth and his friends, trains because he doesn't want to win- he can't afford to lose.
That being said their first fight is dominated by Vegeta, even though he loses the entire battle in the end. He easily won 1 on 1 with Goku but lost to the combined effort of Goku and his friends.
In Freeza saga there isn't much time to train for Vegeta, he mostly relies on his heritage to grow stronger after each battle, there are many unexplained factors why his power grows to absurd levels while fighting Freeza, but almost the same goes to Goku in Freeza saga, so we will skip that, only saying that Goku trained further under heavy gravity, and relied on his Kaioken technique to match Freeza.
Goku returns from Namek with Super Saiyan transformation, while still being stronger than Vegeta in his normal form. Naturally Vegeta does his best to catch up, while Goku basically wastes 3 years training with Piccolo and Gohan, achieving very little gain from those 3 years. Maybe Akira didn't have a good idea what to do with Goku but still for me those 3 years look like a waste on Goku's side.
Vegeta in those 3 years trains his ass off in space, or under 300-500 times normal gravity, he gets his Super Saiyan transformation and is considered stronger than Goku at this point.
Then the training for Androids and Cell begins, Vegeta goes in with Trunks but doesn't care about his son. He tries to unlock more potential of his Super Saiyan form and succeeds, he sees the downsides of Ultra Super Saiyan and trains his Ascended form for many months, it allowes him to fight a decent amount of time with this extra stress on his body.
maybe not as strong as Goku but beats him in badass appeariance
It's a smart way of training, but Goku gets a better idea (maybe thanks to Gohan, seeing him transform for the first time and the amount of stress the kid had to sustain at the moment? Just an idea)- when he gets the Ascended Super Saiyan transformation he sees that the stress it puts on the body is too great to have a long fight, and instead trains himself and Gohan to get the bodies used to Super Saiyan transformation, so when in need they can raise their powerlevels like they normally do in base form, without forcing the transformation to output more power. Thanks to that idea their transformed state has zero energy output when they don't fight, and the ki flow is controlled with amazing precision, to the point where it's pretty much natural to the body. Training in this mastered form with his son matching his power gave amazing results.
When Vegeta saw Goku quit the chamber he was stunned by 50% of Goku's power. He reentered Room of Spirit and Time alone to close the gap, which he was unable to do- he was training alone, had to figure it out himself and I guess this is a good point to state another difference about Goku and Vegeta:
Goku is a martial artist, while Vegeta is a solider. Goku got a lot of training and discipline from his teachers, he understood the ki control more than 7 years before Vegeta did, he treated ki as a vital element of his life and body, while for Vegeta it was more like a weapon, tool and a measure of power. These teachings, understanding of ki and training his son were major factor why Goku's trainings were more beneficial than Vegeta's.
Second visit in Room of Spirit and Time had only a slight impact on Vegeta, he started to master the Super Saiyan transformation but it took him way more time than to Goku, he was unable to finish this training in the chamber. I had my own theory (looking how in the manga he faces Cell in his SSj state and in the anime he's using ASSj) that he somehow mixed Semi-mastered Super Saiyan with Ascended, but my theory was mostly for covering flaws in my own numbers when it comes to those transformations so again- just an idea.
Vegeta looked terrified how strong Goku and Cell became, and became training while enjoying life on Earth.
7 years have passed, in which both trained hard, Vegeta on Earth, Goku in the other world. Vegeta managed to get much closer to Goku (which had a headstart considering how strong he was in Cell saga), but was still unable to become stronger. Maybe the gap was too big to close in that period of time, maybe King Kai's methods and a body resistant to time passage had a major factor in it. Vegeta's mindset was changed, now he also has a family and people to protect (as he stated himself watching Goku fight Kid Buu).
Vegeta managed to close the gap between him and Goku thanks to Babidi's power-unlocking technique, but still lacked Super Saiyan 3 transformation to match Kid Buu or Goku in power. Still, Vegeta had a major character developement in those years, which culminated when he gave his life to protect Earth and his family, exploding and trying to take Majin Buu with him. It's also very important that Vegeta saw Super Saiyan 3 flaws, greatly reminding Ascended/Ultra transformations which will be important later.
"I'm not going to hell alone, I'm taking You with me!"
And now he jump to recent happenings in Dragon Ball. There are many differences between the 2 movies and the manga so it won't be easy to connect all that but the most vital points are:
Goku fights with Beerus, not being able to land a hit on him and being knocked out by 2 hits. It's very possible that Beerus is using more of his power than when fighting Vegeta and Z warriors on Earth.
In the movie Vegeta fights Beerus in his SSj 2 state, Beerus states that Vegeta is a veteran fighter, even if he's much weaker than him. Then when Beerus slaps Bulma, Vegeta gets a second wind and powers up way more, being able to land a few hits on Beerus. I think everyone states that he surpasses Goku in this moment, finally being stronger than him and I love it.
I have my own theory for this case- Vegeta saw how flawed Super Saiyan 3 was and skipped that transformation, instead he focused on Super Saiyan 2 and tried to master it in the same way Goku did years before with basic Super Saiyan. I cannot tell how successful he was in that attempt, but I like to see his outburst as a Super Vegeta 2, or Ascended Super Saiyan 2 transformation, his own variation of mastering and ascending the SSj2.
From this point Vegeta is more mature fighter than Goku is, also noticably stronger. Goku is being scolded by Beerus that he's selfish in his God power (Goku doesn't like it, since it's not his own power he's using) while Vegeta was able to sacrifice his pride in order to defend the Earth (might be a bigger sacrifice than his life in Buu saga :P ).
Then Freeza returns, while both Goku and Vegeta train with Whis. Whis scolds Goku for letting his guard down and generally being too relaxed, while Vegeta is being scolder for being too focused on fights, overthinking them and thus being slower to react.
At this point it's easy to say that they are matched in strength with Goku or Vegeta is even more powerful. This post is so long that I think I forgot the summary, as I posted parts of it in between sagas D:
The point is that while Goku was weaker than Vegeta, he was able to push his pride aside and train under masters, while also having pure intention in his fights. Vegeta was born as a elite warrior, didn't receive any martial training from anyone and due to his pride he was stubborn to learn or receive help from others to get stronger. It took him years to change that mindset, but when he did he proved himself to be as strong or even stronger than Goku. Goku didn't get as much character developement in DBZ, it's nice to see it change in DBS. Both are great rivals, pushing themselves further in their trainings to the point where they spent 3 years together training in a new Room of Spirit and Time. Time will tell how strong they got after that, but in my opinion chances are high they got stronger than Beerus.
with enemies like these You don't need any friends
I consider the subject over for now, but I just have to add how much I love this franchise. I've been a dragon ball fan since I was 5 so I get a 20th anniversary in 2016. No other franchise had that much impact on my life and I doubt I will ever stop being a Dragon Ball fan, it's a part of who I am today. Thanks for reading and insisting to write about what I love the most, this is not a blog for Dragon Ball posts but I'm starting to think about another, Dragon Ball related one.