Is a 16 gauge shotgun more powerful than a 12 gauge shotgun?

No. A 12 gage shotgun shoots a larger charge than a 16 gage. Shotgun sizes were designated according to the number of steel balls that could be dropped into the barrel that would weigh a pound. 12 steel balls weighing one pound would be dropped into a 12 gage shotgun. Thus it is a larger size than a 16 gage.

(Do not waste your money on a 16 gage shotgun, at least in the United States. You will have difficulty finding shells. You should get a 12 gage or a 20 gage.)