A standard 12 gauge load will throw 1 1/8oz of lead shot.
A standard 20 gauge will throw 7/8oz of lead shot.
12ga shells are capable of handling IIRC up to 1 1/2 oz in the really stout loads in a 2 3/4" hull.
A 20 gauge about 1 1/8oz is the max possible in a load of shot in a 2 3/4" hull.
Many people that are target shooters are loading down in the 12ga to 7/8oz of shot for recoil and comfort reasons, the same is done in 20ga shells, bringing them down to 3/4oz of shot.
The effectiveness is slight. For defense, inside 20yards, either load will kill just as dead. For game hunting the 12 has an edge, although slight. For waterfowl with steel loads the 12ga has more advantage.
My personal favorite is the 28ga throwing 3/4oz of shot. 80% of my shooting is with this remarkable little shell. I have several 12gauges, but I keep an 870 20 gauge handy in the house for unexpected circumstances.