Cooler wins . When cooler was introduced he was in his final form. Freiza went thru 3 transformations to get to his final form. Which was the same form as cooler. Cooler than progressed to a higher form than freizas. Freiza got his body reassembled with some metal plates it didn't really give him a power boost.
Thats why there's a new dbz movie where freiza reveals a new transformation. Key word *new* ..
Anyway cooler beats freiza everytime until Freezers *NEW* transformation is revealed
Cooler > Freezer > Chill > Cold ( cold is last because he showed no feats, and lost to a super sayian trunks with no fight at all)
The "final" or "fourth" forms that Cooler and Frieza display are their true forms, it was said Frieza had to make surpressed forms just to keep his power from destroying his body. So, Frieza going through them is just a show of his lack of control/high power level.
Mecha Frieza was said to be stronger than a regular Frieza, even if it's by a slim margin. There's a difference, but Cooler in his Fourth form never displayed the same level of power as Frieza, and seemed to always be going at Goku at his max when in his fourth form. One could say it's because Goku post Namek > Namek Base Goku. But, it shouldn't be to that degree.
A hundred percent Mecha Frieza should logically be able to compare to a Fifth Form Cooler; Just going off that a Fourth Form Frieza's displayed better feats of strength against a foe of around the same level. And, Cold was said to be stronger than Frieza in his suppressed state. Even if his transformations aren't the same as Frieza, he still has a true form where his power'd spike.
TLDR; King Cold > Fifth Form Cooler>=Mecha Frieza > Frieza > Cooler.