I'm hesitant to using characters to determine power boost because I mean I think power increases that were 2x were deemed as inconceivable. What I would love to do is try to gather all statements of every form that doesn't have a multiplier and see if we can gauge whether it's a big increase or small increase. I did some research of my own using the DB and DBS Manga to see what could be inferred. Nothing solid but info nonetheless.
Super Saiyan 2
Consistently SSJ2 on its own has been viewed as a not too significant increase when compared to greater power.
Babidi in comparison to Boo remarks that there wasn't much of a change at all between SSJ1 and 2. (DB Chapter 473 ~ Goku meets Boo)
Beerus was unimpressed in the manga and questioned if that was all Goku had to offer. Later in the spar against Trunks and Goku, Beerus had to make sure if it was SSJ2 version to which Whis responded with "Most Likely" clearly showing that they don't see a huge difference between SSJ1 and SSJ2. (DBS Chapter 2 ~ Goku's Defeat and DBS Chapter 14 ~ SOS From The Future)
Zeno was even confused on if he changed or not stating he felt no real difference between SSJ and SSJ2 (DBS Chapter 29 ~ Toppo, Universe 11 God of Destruction Candidate!)
Only when its powered up by rage (in the case of Gohan's initial SSJ2 transformation and Vegeta's Rage against Beerus) or special training (In the case of Trunks) does it seem to garner some level of attention.
Super Saiyan 3
SSJ3 is pretty much viewed as otherworldly and is the Pinnacle of Saiyan strength outside of character specific amps and transformations being taken account. In canon with its mere power being felt throughout the Universe, the residual ki shaking the entire planet itself, in the movies shaking even the Massive Afterlife. This power is almost always looked at as a massive or impressive increase:
All of the Z cast were in utter shock at the increase and incredible power of the SSJ3 transformation, from Roshi not even recognizing Goku in comparison to his prior power, Gohan mentioning that it was impossible for it to be Goku, Kibito also mentioning that his ki being felt from the Kaioshin Realm was unbelievable. (DB Chapter 474~The Limit, Super Saiyan 3)
Babidi now concerned that Majin Boo, his once invincible monster in comparison to SSJ2s, would be destroyed by this new power (DB Chapter 474~The Limit, Super Saiyan 3)
Vegeta in the Buu Saga remarked he couldn't even come close to SSJ3's power though he fought evenly matched with Goku's SSJ2
(DB Chapter 509~Battle For The Universe)
Beerus remarking that the form was a "not bad" increase on the lackluster SSJ2 (DBS Chapter 2~Goku's Defeat)
Trunks mentions that the power of SSJ3 seemed "impossible", meaning the increase has to be far greater than the jump between SSJ and SSJ2 and maybe one can make the argument of being better than the gap between Base and SSJ2. (DBS Chapter 14 ~ SOS From The Future
Zeno now states that Goku looks scarier and more entertaining in his SSJ3 state than in his SSJ2 form. (DBS Chapter 29 ~ Toppo, Universe 11 God of Destruction Candidate!)
So overall though we don't have definitive multipliers we do have consistent responses that should give SSJ3 afar greater a boost than any other transformation prior.
Super Saiyan God
SSJG has been pretty much the gap closer between Goku and Vegeta and god tier fighters. This power put them feat wise in the realm that was typically attributed to only Destroyers. Where SSJ3 appeared other worldly in most cases, SSJG is just in a realm seemingly unreachable (at first).
Goku states SSJG is a world of power he's never felt before, putting SSJG higher than even his fusion into SSJ Vegito (only regarding to that power at the time since Vegito is exponential depending on both of the fusion participants' potentials) this should actually put SSJG at a 50x SSJ3 at least actually. (DBS Chapter 4 ~ Battle of Gods)
Beerus and the other gods seem to be impressed with Goku's initial SSJG power fearing the entirety of the Universe would be destroyed simply by the mere clashing in power and Beerus touting that it has been the hardest he's ever tried in a battle (which I know isn't saying much but in comparison to SSJ3 its something I guess.) (DBS Chapter 4 ~ Battle of Gods)
SSJG Goku was roughly greater than a tenth of the power of incomplete Super Saiyan Blue Vegeta in the manga and took a Goku who in SSJ was getting worn out by a Hit that clapped SSJB Vegeta to him basically stomping Hit till he increased his Time Skip abilities.
(DBS Chapter 13 ~ A Winning Universe Decided)
Goku states in his fight with Toppo that pass SSJ3 he would be in an entirely different world of power once transformed into SSJG and Beerus mentions that he's actually a match for Toppo who himself powered up with god ki from his Base form which was stomping SSJ3. Meaning the gap between SSJ3 - SSJG is greater than the difference of Base Toppo and Toppo with divine energy. (DBS Chapter 29 ~ Toppo, Universe 11 God of Destruction Candidate!)
This is pretty much what I can dig up on the forms using the DBZ and DBS Manga, I'm sure there's statements and feats in the anime and the non canon material like GT and the movies not to mention video games and stuff.
That thread was utter garbo. Had this hooligan made it first over the High 3-A thread he may have had some staff support because we didn't have like 4 CRT backing up the rating.
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