I'd say it depends on what is you definition of best. That being said, I shot my first turkey with a 2 3/4" 20 gauge. Then, as I got older, I used a 12 ga 3", then a 12 ga 3 1/2". And I got my share of turkeys with them. I consider them to be the most versitile.
However - since I've grown older and wiser. And I am getting better at getting old Mr. Longbeard in closer, and with the improvements in turkey loads, I switched back to a 3" 20 Ga. In truth, I actually got a Rem 870 youth model. This shotgun is very light compared to my 870 12 ga, shorter so it fits me better when sitting and the 3" payload is plenty for turkey out to 30 yds. once you find the right load for your individual choke.