Disclaimer note: This theory is based on non-canonical information and is merely a speculation. Constructive criticism is welcomed.
The topic: Is Cooler really stronger than Frieza? How strong is Cooler? While this topic is long since dead, I thought I would revive it for shits and giggles after developing a reasonably solid theory.
The Cooler movie is technanically non-canon and therefore doesn't fit in with the main story, but for arguments sake I have placed it within the same universe and timeline as the DBZ series. With this considered, it is likely the events within the movie took place some time after Goku returned from Namek and was in the process of training against the Android threat, just after the death of Mecha-Frieza and his father.
It is generally assumed that when Goku left Namek he had a base power level of roughly 3,000,000. After reaching Yadrat and returning to full health, Goku would have recieved a large Zenkai boost from his battle with Frieza. I'm led to believe that the Zenkai boost, along side any training Goku did over the course of his stay on Yadrat, rose his power level to anywhere between 6,000,000 to 9,000,000. After Goku returns to Earth, it is also likely that he performed some training before Cooler's arrival took place, meaning his power would have increased even futher. When Cooler critically wounds Goku with his Darkness Eye Beam, it is assumed Goku recieves another massive Zenkai boost, placing his power anywhere between 12,000,000 to 16,000,000 at base. Despite all that being said, Goku's base increase of 16,000,000 should have been no match Cooler's apparent power of 140,000,000 (as Cooler is stated to have had a power level that was higher than Frieza's full power form by 20,000,000). So, why was Goku in base form evenly matched with Cooler in his 4th form?
Well firstly, I believe that when Goku first attacked, Cooler was only exhibiting a very small percentage of his full power (roughly 2%), placing his power level at around 2,800,000. Why? It is possible Cooler assumed that his brother had been killed in one of his lower forms, when he was weaker and more vunrable. Cooler had mastered control over his ki and was thus able to maintain his true form at all times; he likely pressumed that in his 4th form, the enemy would stand no chance against him, meaning he wouldn't have to exert full power. Futhermore, when Cooler defeated Goku with a single blast prior, he probably thought that Goku posed no threat to him. After being taken by suprise, Cooler began raising his power to about the 10,000,000 mark before ending his skirmish with Goku. At this point, Cooler, rather than toying with his opponent the way Frieza did and raising his power in gradual intervals , decides to morph straight into his final form and kill Goku immediately.
While Cooler's exact power in this form is unknown, unreliable sources such as the Shonen jump magazines state he sits around 470,000,000. I think this estimation is reasonably accurate as it explains why Cooler dominated Goku initially, but lost to Super Saiyan so easily. Assuming Goku's power is around 12,000,000 to 16,000,000 at base by this point, his times 20 Kaioken technique would place his power at 240,000,000 to 320,000,000 respectively. This presents a 230,000,000 to 150,000,000 power gap respectively between Goku and Cooler, explaining why Cooler dominated Goku so easily. When Goku transforms into a Super Saiyan (times 50 boost), his power level would be between 600,000,000 - 800,000,000; this presents a 130,000,000 - 330,000,000 power gap between Goku and Cooler, explaining why Cooler couldn't even harm Goku in his Super Saiyan form. To top this off, Goku would have had much greater control over his Super Saiyan form, unlike when he fought Frieza as a newly transformed SS.
If we compare this information with Frieza's fight against Goku on Namek (back when Goku had a base power of 3,000,000), we can see an great difference in power gaps. Goku's times 50 transformation (SS) would have placed his power at 150,000,000, while Frieza's had a max power of 120,000,000. This only leaves a gap of 30,000,000 between the 2 fighters, which would explain why Frieza was able to hold his own for awhile. On top of this, Goku was a newly transformed SS and hadn't gained full control over his power yet, meaning he would have been weaker while fighting Frieza.
With all this in mind, I theorise Cooler was indeed exponentially stronger than Frieza at the time of his movie, but stood no chance against a post-Yadrat, double Zenkai boosted, and heavily trained SS.
Holes in this theory:
- Cooler states to Goku "As you already know, I am in the 4th transformed state..." This would lead us to assume Cooler was aware Goku defeated Frieza in his true form, meaning Cooler had no reason to exert minimum power. However, Cooler's early victory over Goku (when he wounds him with the Darkness Eye Beam), may have promted Cooler to underestimate his opponents true strength, thinking him to be still weakened by the earlier attack.
- It is likely this movie is set in an alternate universe to the main story; comparing Cooler from this universe to Frieza from another universe would be redundant (there could be a Frieza in the same universe as Cooler who's power is much greater).