As much as I am fond of the .410, and I am, the 20 is a better choice if you have only one gun. More shot in the pattern is not a bad thing. There are more different loads for the 20 gauge and ammo for the 20, in general, is less money than for the .410.
Modified choke for general use and nearer rather than further turkeys. You can, however, get an H&R Pardner 20 gauge with screw-in chokes and be able to match the choke to the task.
Pete