Here's an interesting to watch video on the subject:
All fun aside, the major difference in shotgun gauges is the ability to carry a payload. The 12 gauge can
carry a larger payload than a 20 gauge (Smaller Gauge Number = Bigger Payload). Can
is an important word here since you CAN buy light load 12 gauge shells that carry less payload than a heavier load 20 gauge. This article does a nice job of laying it out:http://randywakeman.com/ShotgunPowertheMyth.htm
In general, you'll have an easier time finding a wider variety of shells for a 12 gauge than a 20 gauge, but that does not mean you don't want both. For some shooting, the lighter payload typical of the 20 gauge is more appealing, less game damage, more challenge to busting clays, etc.