Reposting my edit because new page:
It is a huge increase, though Super Saiyan God is not a set multiplier and works in mysterious ways. Goku retained the power from Super Saiyan God, putting his base at 2,400,000,000 in order for Godly Ki + Super Saiyan 1 to equal Super Saiyan God for the end of his fight against Beerus. Goku got stronger from there and absorbed more Godly Ki from the Godly HTC, turning his Super Saiyan with Godly Ki a lovely shade of blue.
Toriyama stated that if someone else were to become Super Saiyan God, their strength as the God would depend on how strong they were before. Sounds just like the other forms to me.
I no longer believe in the two base theory because Universe 6 has shown no evidence for it. Given that Goku/Vegeta didn't look very impressive in their base forms in Universe 6, and Super Saiyan 1 wasn't seen or referenced at all during the time of the RF movie/arc, I think there's been a retcon.
The RF script described Super Saiyan Blue as Super Saiyan, and just described the new features in Goku's appearance. Even in the movie Vegeta just calls the form Super Saiyan. The Heroes cards don't allow transformation into Super Saiyan 1 until the promotion for Universe 6, where they are explicitly connected to that arc.
Then in the manga, when Goku and Vegeta are sparring Vegeta jumps straight to Blue to get an advantage over Goku.
I feel like the original intent was that Super Saiyan Blue wasn't a separate form but the same form that had been altered. Then they can go Super Saiyan again, don't seem to be that much greater than Piccolo (who hasn't been said or shown to be significantly different) and stop doing ridiculous feats.
Frost in the manga was told if he trained, he could become stronger like Freeza did, so I don't think the lack of Ultimate Evolution is the only area he's weaker on - I don't see his untrained Final Form being stronger than Freeza's trained Final Form.
To me it would appear that Goku and Vegeta are being portrayed at base/Super Saiyan at a 'normal' (ie pre-BOG) level with Super Saiyan Blue being the only God-tier power they have. Fighting on par with untrained Freeza Clan and non-Godly Saiyans makes it seem to me they're back to a more reasonable level.
There's not an in-universe explanation for why they'd revert, but it wouldn't be the first time. Goku after absorbing Super Saiyan God was able to fight on par with Super Saiyan God Goku, but after that he was portrayed as being much weaker than Beerus without Super Saiyan Blue (even to the point where Whis compares their difference in power to a 3 metre tree versus a 100 metre tree).
Assuming Goku and Vegeta are still Godly strong without Blue just causes a massive power bloat among all other active characters, including the othwerwise unimpressive Universe 6 fighters.
Well, even if Goku and Vegeta are inexplicably back to being ~Buu Saga level aside from Super Saiyan Blue, Frost should be more around Cell's level than Freeza's level, considering he's still stronger than Piccolo.
EDIT: Nevermind, you specified Freeza's trained Fourth Form being stronger and I agree with you on that front: Frost's Final Form should be weaker than Resurrection 'F' Freeza's Fourth Form.
edited 3rd Apr '16 5:10:30 AM by PushoverMediaCritic
Yeah he'd be stronger then the untrained Freeza (barring other potential weirdness like all the crap surrounding Tagoma/Shisami) but the difference wouldn't be so huge since he's much weaker than Super Saiyan Goku.
I just think it'd be too coincidental for Super Saiyan Goku/Vegeta and Piccolo to have a gap that fits what they had in the Boo arc or for Goku to know how Piccolo would fair without seeing the results of Piccolo's training if Piccolo got a major, unmentioned power-up.
Edit: To elaborate on Shisami/Tagoma, back when Resurrection F came out it wasn't known if Shisami had grown a lot stronger from his original Zarbon tier level or if Piccolo and base Gohan had been reduced to below Zarbon tier via retcon/continuity error. Then when Super changed it to Tagoma and revealed he trained with Freeza, it seemed like Tagoma just grew really strong, but then he's said to surpass the Ginyu Force which might mean that Piccolo/base Gohan were still retconned below Ginyu Force level.
If that kind of mistake was possible, then Piccolo and Goku's massive advantage over regular Freeza might have also been missed and they were written in those fights as being around Freeza's level. The idea that Super Saiyan Goku's advantage over Freeza hasn't grown all that much isn't something that's really knew either, even if it's clearly wrong following the manga.
There's not much evidence to suggest it in this case, it's just something I found interesting to think about.
edited 3rd Apr '16 5:23:09 AM by Saiga
It's just Goku's base >/= 4th Form Freeza > 3rd Form Freeza > 2nd Form Freeza > 1st Form Freeza > SS1 Gohan > Ginyu in Tagoma's body > Tagoma = Gohan's base > Piccolo from the very last arc that really sticks in my craw as a problem, provided no really stupid retcons about how strong Gohan and Piccolo are.
edited 3rd Apr '16 5:26:34 AM by PushoverMediaCritic
Actually, would all the continuity problems be fixed if Resurrection 'F' and its associated arc in Super never happened? Establish that Goku and Vegeta have been training with Whis and have gotten a little stronger, but both have managed to harness and control Godly Ki using Super Saiyan as a conduit. Goku and Vegeta are both about as strong as SS1 Trunks was when he first arrived in base, and have the Super Saiyan forms, as well as Super Saiyan Blue as a trump card. Super Saiyan Blue wouldn't even need to be stronger than Super Saiyan God, it could actually be a bit weaker to allow Goku and Vegeta more room to grow.
Preach it spidey.
Even the fucking writers are caught up in Power Level wanking.
It truly is the bane of all things. A shame too. I really wanted to enjoy super. Ah well, I'm just gonna not think about all that shit and take everything at face value.
One Strip! One Strip!Who says it's not canon?
Arale is a joke character who does whatever she pleases. She easily beat a dude that Goku had trouble beating.
Dr. Gero stole some of Arale's specs to help him make the androids
This is now my personal canon.
Now you've started a thing IANCE. I hope you're happy.
So, is it just me, or does it seem like Hit is a Stand User?
All this talk about invisible attacks that no one can see and his comparatively strange attacks to everyone up to this point does make it seem like he's doing something interesting, though.
edited 3rd Apr '16 10:10:40 AM by Hobgoblin
Watched the ep.
Nothing much to say. Bring on Hit. We won't really know what he's capable of until Goku steps up (since Vegeta has to be a little tired by now), but we'll get a better look at his abilities.
Interesting that he wants the box. Will that be important later?
One Strip! One Strip!

Oh,I thought you meant vs Godku.I see.