Dragon Ball Z Kai will also be used for anything the manga does not cover. DBZ Kai is called the "Toriyama Cut" in Japanese material, so we should consider what it presents as valid. It is also used whenever the Dragon Ball Super anime shows a flashback, so the DBS anime follows the continuity of Dragon Ball Z Kai, and as such this power scale is in regards to that continuity.
Power Gaps:
Two fighters that have a 1.25x gap between them are said to be "rivals." Nappa says a Saibaman "rivals" Raditz. A Saibaman has a power level of 1,200, while Raditz has an official power level of 1,500. That is the same gap as SSJ Goku against 100% Freeza.
Gaps larger than 1.25x have been shown to end quickly in favor of the stronger fighter. Vegeta at a power level of 24,000 easily killed Cui, who had a power level of 18,000.
This is further substantiated when Recoome, who should have a power level of more than 40,000, easily defeats Vegeta, who was over 30,000 at the time. That is a minimum of 1.33x gap, but likely larger.
We can deduce that gaps larger than 1.25x exit the range of the two fighters being considered "rivals" and considerably favor the stronger fighter.
Official Freeza Saga Power Levels:
True Form Freeza:
~50%: 60,000,000
~100%: 120,000,000
Goku:
~Base: 3,000,000
~SSJ: 150,000,000
This establishes the baseline. These are the official power levels for the Daizenshuu, and as such they are valid.
Mecha Freeza Arc:
To start with, here are the character bios for the Mecha Freeza arc from the Daizenshuu:
We should note that Future Trunks' bio says Freeza "gave Goku a difficult fight." The gap between 100% Freeza and SSJ Goku is 20%(Freeza is 20% of Goku), while from another perspective Goku is 1.25x Freeza's power level. This fits with the known rivaling gap.Freeza
"Even at his full power, he was completely defeated by Super Saiyan Goku. He attacked Earth after becoming Mecha Freeza, but was pulverized by Trunks." -Daizenshuu 7, Human Racial Dictionary
Future Trunks
"He possesses tremendous battle power, cutting Freeza in half with a single slice, who had given Goku a difficult fight. However, being no match for the Artificial Humans, he goes to the present to train." -Daizenshuu 2
And some quotes from both Strength Checker and Dragon Ball Z Kai:
Freeza's expectations of Saiyans:
Freeza knows Saiyans get stronger, so it is reasonable to believe Freeza would expect Goku to improve after the battle on Namek.Chapter: 264 (DBZ 70), P6.5
Freeza: “It seems that the Saiyans really do hide bottomless battle power…It increases greatly the more they battle…Of course, there’s no way they could be a match for me, but if I don’t think of the future and nip them in the bud now…After all, it’d be troublesome if they were able to become Super Saiyans…”
Mecha Freeza's Power:
What this tells us:Chapter: 329 (DBZ 135), P11.5
Kuririn: “Did you feel it, Gohan!? That absolutely incredible ki!”
Chapter: 329 (DBZ 135), P14.1
Cold: “A small planet…Wouldn’t it be better if you just wiped it out in one shot?”
Freeza: “That wouldn’t satisfy me…I want to make [Goku] well acquainted with my powered-up self…”
Chapter: 330 (DBZ 136), P9.7
Yamcha: “So this guy called ‘Fr…Freeza’ has such terrible…ab…absurdly large ki…?”
Gohan: “This isn’t it…he gets much, much stronger…!”
Chapter: 330 (DBZ 136), P10.3
Yamcha: “Wh-what are you going to do when you get closer?...!! They’re un-unbelievable monsters, aren’t they? And…and there are two of them!! It…it’s hopeless, isn’t it?...!!”
Chapter: 330 (DBZ 136), P13.3-4
Cold: “The Earthlings don’t matter, but the Super Saiyan alone we absolutely must exterminate, by any means. The one who holds the greatest power in the universe must without a doubt be our clan”
Freeza: “We can definitely defeat him if we go at him together, Papa. And I’ve powered up too, so I think I can probably go alone.”
Chapter: 331 (DBZ 137), P3.5
Freeza: “It’s an honor that my name should be known on this planet so far removed from the rest of the galaxy…However, unfortunately you don’t seem to know that I have the greatest power in the universe…”
1. Mecha Freeza is more powerful than Namek Freeza overall.
2. The power the Z-Fighters sense is not Mecha Freeza's full power. Since the Z-Fighters don't know Freeza has powered up, Mecha Freeza's suppressed power level would be a decent amount lower than his full power on Namek.
3. Mecha Freeza and King Cold fighting together would surely beat the power that Freeza expects Goku to achieve since Namek, but Mecha Freeza could 'probably' do it alone.
100% Mecha Freeza > Expected SSJ Goku > SSJ Goku(Namek) > 100% Freeza >> Suppressed Mecha Freeza
Now for King Cold:
The quotes from the manga don't make a comparison between Mecha Freeza and King Cold, but rather simply mention King Cold is absurdly strong. However, in DBZ Kai, King Cold is mentioned as being stronger than suppressed Mecha Freeza:Chapter: 329 (DBZ 135), P11.5
Kuririn: “Did you feel it, Gohan!? That absolutely incredible ki!”
Chapter: 329 (DBZ 135), P12.3
Tenshinhan: “It…it’s not just one…There’s another absurdly large ki…”
Chapter: 330 (DBZ 136), P2.3-4
Gohan: “Ku-Kuririn-san, did you notice it!? F-Freeza and ano-another large ki that resembles Freeza…!!”
Kuririn: “Y-yeah…There’s no way I couldn’t notice…ki this huge and gaudy…”
Chapter: 330 (DBZ 136), P10.3
Yamcha: “Wh-what are you going to do when you get closer?...!! They’re un-unbelievable monsters, aren’t they? An…and there are two of them!! It…it’s hopeless, isn’t it...?!!”
Mecha Freeza(Full Power) > Expected SSJ Goku > SSJ Goku(Namek) > 100% Freeza(Namek) > King Cold > Suppressed Mecha Freeza
Next is the arrival of Future Trunks, and scaling his power.
Base Form Future Trunks:
Future Trunks is suppressed, of course. In DBZ Kai, after Trunks kills Freeza's men, Krillin notes that Trunks' base form power is tremendously huge:Chapter: 331 (DBZ 137), P4.1
Context: talking about Trunks' repressed power
Freeza goon: “Battle power only 5…miserable trash…”
Super Saiyan Trunks:
Chapter: 331 (DBZ 137), P9.1
Context: challenging Freeza and Cold
Trunks: “Come at me at full power right from the start. I’m not soft like Son Goku…”
Based on Goku's assessment, SSJ Future Trunks should be beyond any rivaling power gap with Mecha Freeza. Some might say it only applies to suppressed Mecha Freeza, but DBZ Kai has the addition that Future Trunks can catch a full power Supernova attack from Freeza with no visible effort.Chapter: 335 (DBZ 141), P3.3-4
Goku: “For you, a Super Saiyan who instantly defeated Freeza and co., to call them monsters is really something…
Trunks “Yes…I’ve stood against them, but unfortunately…In any case, I’m up against two of them…Even fighting one-on-one, I could barely manage to escape…”
Freeza's first blast against SSJ Future Trunks wasn't full power, but Trunks continues to tell Freeza to use full power, and so Freeza obliges him:
Then Goku returns from Yardrat and spars with Trunks' sword, with Trunks concluding that Goku is better than he expected.
Final Verdict:Chapter: 334 (DBZ 140), P13.3-5
Context: after Trunks and Goku fight
Trunks: “As expected, the rumors were true. No, you’re even greater…This was the sword that cut even Freeza…”
Goku: “You weren’t serious, after all.”
SSJ Goku(Yardrat) > SSJ Future Trunks >> 1.25x Mecha Freeza(Full Power) > Expected SSJ Goku > SSJ Goku(Namek) > 100% Freeza(Namek) > King Cold > Suppressed Mecha Freeza > Base Goku(Yardrat)> Base Future Trunks > Anyone not Freeza or a Super Saiyan