I voted for the 12 gauge.
The only advantage for a 20 gauge would be a lighter gun but you are not going to get as good a pattern out of a 20 gauge as you will a 12. I've never felt weighted down by a synthetic stocked 12 gauge of any brand so there is no reason for me to sacrifice the patterns I'm getting with the 12 gauge.
Nothing wrong with a 10 gauge but quite frankly with the rise of the 3 1/2 inch 12 gauge there really isn't anything you can do with a 10 gauge that you can't do with a 12 gauge now. And there are many more shells and chokes available for the 12 gauge compared to the 10. Lot more models of shotguns offered in 12 gauge to choose from too.