Below is link to the Power Gain Thread where Kabam details the differences in rates (can follow up in there if needed). But to summarize, each additional RANK of the champ dictates the % of additional Power Gain above what is considered the base rate (only Rank matters, not the 4/5/6* Rarity, so 6* will obviously be at a disadvantage in Power Gain).
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https://forums.playcontestofchampions.com/en/discussion/158294/champions-of-different-rarities-gain-power-at-different-rates#latest