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Theory: As everyone knows in DBZ, a Super Saiyan appears every 1000 years. Which is true in my opinion. Alot of people think Goku is the Legendary Super Saiyan. I think he is by default. I think Brolly is the True Legendary SSJ.
Overview:
Brolly is the natural Legendary SSJ and Goku is the default Legendary SSJ. Half breeds can become the Legendary SSJ and Vegeta is a wannabe. So there's my opinion on the Legendary SSJ. Thanks for reading.
Note: These statements are my opinion only.
Brolly- Everyone knows (and if you don't) I think Brolly exist in the DBZ timeline. He had the power naturally, like a chosen one. By birth his power level was at 10,000. And watching Movie 8 his power seem to grow naturally and faster than any normal saiyan (including Goku & Vegeta). He destroyed a planet from another with a ki blast the size of a tennis ball. Just imagine the power he's packing. It's possible he's strong as SSJ 2 or would be reaching that state soon. Just because he wasn't under his father's control no more, his could grow more like it did in Movie 8. Apparently that was the first time he went passed SSJ mode. The other movies like 10 and definely 11 doesn't exist.
Goku- He went through all the levels before he fought Goku & the others such as False SSJ, SSJ, USSJ & USSJ 2. And like the last SSJ, his power was uncontrollable and he was violent (Which Brolly had, lol). Our main saiyan characters had to work to become SSJ's. Look at Goku, he had all the trainers in the universe and the heavens. He was trained by Son Gohan, Master Roshi, Karin, Kami, King Kai, the Yardratians, training in the Room of Spirit & Time and in the underworld of Hades. All the training he's been doing for the past 33 years I think, it's no wonder he's at SSJ 3. I also think because he was born on the same day as Brolly too.
Vegeta- He's no where near a true SSJ. He had to train his butt off and when he first became a SSJ he was lacking a little bit of SSJ power. When he first appeared in the Android Saga as SSJ, he barely had an aura (he had it when he powered up for a moment.). He didn't get his full auru till after he ate a senzu bean (it helped become a full SSJ, lol). Also, Vegeta tried to pull a Goku. On Namek, when Frieza tried to hit Goku with his finger beam, Goku let him. If anybody remember when it hits him in his face knowing what it could do. Goku brought his head back up and wasn't even bleeding. When Vegeta "let" #19 punch him in the face, he brought his head back up, you can see his lip bleeding (weak bastard, lol). As for other SSJ modes, he only got to the 1st form of USSJ. Even though the USSJ 2 makes the user bulker, he probably couldn't reach that stage, like Goku, Trunks & Brolly did. Vegeta couldn't even reach SSJ 2 on his own. He's been training for 7 years and still couldn't make it. He had to use Babidi's magic to transform him into SSJ 2. The sentence I'm about to say doesn't matter, just making a point. In GT (damnit I cuss), Bulma made a device for him to turn into SSJ 4. Ok, it's clear again. So basically Vegeta is not a true SSJ.
Gohan & Future Trunks- Due to the fact that their half saiyan & half human they have alot more power than a normal saiyan, so it's more possible they could become SSJ's before a normal saiyan would. Trunks didn't seem to have too much probably reaching USSJ 2 mode. Gohan was the first to go SSJ 2, cause of his half-breed power. And when Rou Dai Kaioshin released his power, he had the strength of 6 SSJ's, but who knows how strong is that. But Gohan didn't have to transform into a SSJ though, so it doesn't matter.
Chibi Trunks & Goten- The half-breed theory is different with these two. Reaching SSJ mode was natural for them, cuz Goku & Vegeta were already SSJ's when they were born. Going anything higher is possible if they train. They wouldn't have to train as hard as Goku did.