A 20ga is fine for HD. Yes, a 12 is bigger and has more power, but a lighter weight 20 is more than capable. Many argue a 12 gauge is overkill or too much for deer, especially with a modern slug. A 20gauge will drop a 200 pound deer or 200 pound night intruder at ease. The 12 gauge would just make a bigger mess out of it. I have a 20ga with a rifled barrel I use in deer season with slugs, and then I put the smooth bore barrel on it and load it up with buckshot for around the house for the rest of the year. Mine is short, easy to handle, fast on target and has a light on it.
I can tell you I did not like my Mossberg 20 gauge and got rid of it. I replaced it with Remington 870 youth combo and this gun is much better. The difference was loading 3 inch shells. Easy with the Remington, fussy with the Mossberg. It has to do with how your (in my case fat) thumb may or may not fit in the given opening when sliding the shells in.