12 Gauge is a bigger (larger diameter) shell that holds more powder and more pellets/shot than 20 GA. Generally speaking, 12 GA is more powerful and much more common to find than 20 GA. Now, there are some low power 12 GA shell that is less powerful than a 20GA but generally speaking 12 GA will be more powerful given the same style of shell. Remember, the smaller the GA, the bigger the shell. I personally would go with 12 GA as it is easier to find and will work better for sporting. I hope this helps.

The quick easy answer is the difference in recoil (how hard the gun is thrust back into your shoulder) 12 Ga is a heavier more powerful round, so therefore is going to recoil a bit harder, 20 Ga shoots a lighter projectile and won't slam as hard into the shooter so it can be better for new or inexperienced shooters, 20Ga while not as powerful is still highly effective as a home defense, or hunting caliber
A more detailed comparison here
wideopenspaces.com/12-gauge-vs-20-gauge-which-shotgun-is-better/