Frieza at 100% in his 4th form had a power level of 120,000,000. When Goku fought him as a SSJ, he had a power level of 150,000,000 and his base form was 3,000,000 (50x multiplier for SSJ).
Cooler in his 4th form has the power level of 104,500,000, and his 5th form had a power level of 470,000,000. When Goku fought him as a SSJ, he had a power level of 500,000,000 and his base form was 10,000,000.
Goku had become much stronger during his time training in space. Cooler obviously knew what he was facing when he fought Goku in his base form wasn't Goku's true power since he beat Frieza, hence why he transformed despite being stronger than Goku's base form.
Regardless, it's been established that a flaw Frieza used to have (prior to the ToP) was that he was so powerful that he never had to train or face a real challenge. As such, he never learned to properly regulate his energy and he burned it off too fast. He compensated for this by staying in his 1st form. This was the same problem he faced when he achieved his Golden form, only with it he burned off energy even faster.He trained himself to properly regulate his energy while in Hell after he was killed again.