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The only time Vegeta was actually stronger than Goku was during the Saiyan Saga. After that, Goku surpassed him each and every time. Here's the math:
Saiyan Saga:
Goku: Returns to Earth with a power level at 9000 (actually 8000 in the manga), boosts upwards of 30,000 with the KaioKen x4.
Vegeta: Has a power level a little over 20,000. Was revealed in the Frieza saga.
Namek Saga:
Goku: Thanks to the Saiyan Near Death Effect, his power goes from 9000 to 18000 when he leaves Earth. During his 100x Earth Gravity training and using the NDE, he makes it to 180,000. After the Ginyu debacle, the NDE shoots his power to about 300,000. During the Frieza fight, he uses the KaioKen x20 to go over 6 million, and when he goes Super Saiyan, he ends the saga at a cool 15 million (SSJ adds a 2.5 multiplier to one's abilities and power, so it seems.)
Vegeta: Thanks to the NDE, he starts the arc with a nice 40,000. After his fight with a transformed Zarbon, the NDE multiples it (probably) around 80,000. After his fight with Reccome, the NDE shoots him up 160,000, and after getting power blasted by Krillin (Vegeta's idea, after figuring out how Goku got so powerful) and healed by Dende, Vegeta ends the arc at just over 320,000.
Androids and Cell Saga:
This is actually the point where things get murky in regards to power levels, since no one uses scouters anymore and we're never given concrete numbers. Based on the ending numbers from the Namek Saga, how much power their training might add, and judging by how their respective fights go, we can sort of get a semi-accurate estimate for each character. (Note, power levels are given as /. Number on left is normal mode, number on right is Super Saiyan.)
Goku: Starts off at just over 6 million/15 million, and not much more given his training with the Yarblecks was more mental than physical. After three years of training with Piccolo and Gohan, Goku is probably sitting at around 8 million/20 million. After getting pummeled by Android 20 and the heart disease, the NDE would have shot him to over 16 million/40 million. Thanks to training with Gohan for a year in the Hyperbolic Time Chamber, Goku goes to fight Cell with somewhere in the neighborhood of 20 million/50 million, which is evident by the fact that he almost keeps pace with the bug man every step of the way.
Vegeta: After being resurrected, Vegeta ends up on Earth with a cool 320,000 (NDE doesn't go into effect if you're dead.) After three years of training and attaining SSJ, it's probable that Vegeta is sitting somewhere close to Goku, if maybe a bit behind. Possibly around 7 million/17.5 million. He gets trashed by Android 18, but not enough to trigger the NDE. He then goes into the Hyperbolic Time Chamber with Trunks, and after some brutal self improvement, is possibly sitting at where Goku was before going into the Chamber (16-17 million/40-43 million), which is where he's sitting at the end of the Cell Games.
I'm not even going to get into the possible numbers during the Majin Buu Saga, because that's where things get insane (SSJ2 everywhere, Majin state, SSJ3, the Potara fusion.) Plus, again, there's no real accurate measurements of their power levels beyond Namek. I've heard it said that Toriyama claimed in the later sagas, it's not even possible to calculate their power because it's so damn high. But it's still a safe bet to assume that Goku is always going to be the stronger, thanks to plot armor.
And thats basically the whole reddit comment thread here on steemit summarized for you wow 45,400+ upvotes and countingon reddit cant wait for steemit to get this popular
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