Huge Power is actually the better one here. Thick fat is great Defensively, but Huge Power DOUBLES you Attack stat. Azumarill's base 50 Attack stat skyrockets to a 436 Atk stat, with EVs, positive nature, and 31 IVs. The power you receive when having Thick Fat is quite low, but is good defensively.
Power: Huge Power
Defense: thick Fat
Recommendation: Huge Power