I have the 12 gauge and use Hornady SST slugs. Here are the ballistics from their website.
12 gauge at 200 yards.
1341 feet per second
1198 ft lbs of energy
6.7 inches of drop when sighted in at 150
20 gauge at 200 yards.
1212 feet per second
815 ft lbs of energy
8.2 inches of drop when sighted in at 150
Clearly the 12 gauge is better not that the 20 won't do the job