With a shot gun there is no advantage to a longer barrel in obtaining tighter or more accurate shot patterns. That is all in the choke that you use no matter the barrel length. The pellets are not being stabilized by the barrel in any way.

You may or may not increase the velocity of the load with a longer barrel but how much velocity do you need to smack a turkeys head at 30+- yards?

I would opt for the shortest barrel offered for the ability to move if needed.