For many years my primary turkey gun was a side-by-side.
Started using that gun back before the "specialized" turkey guns & chokes became popular.
It was factory bored extra-full (left) and full (right), and did a great job out to about 40 yards, even with just 2 3/4" chambers.
Even though I liked the idea of loading the tighter choked barrel with smaller shot (head shot) and the other barrel with larger shot (body shot), I usually just loaded both with #5's because with that gun, #5's would pattern almost as dense and even more uniformly than #6's. Since the #5's would easily break wing and leg bones, usually didn't see the need for going to #4 pellets.
The ONLY reason I've about quit using that gun for turkey hunting is because I wanted to use an optical sight, which was not easily mounted on a side-by-side. If it had been practical to mount a low-power scope, I'd probably still be using it, and feel little "handicap" by the 2 3/4" chambers. Over the years, most turkeys I've killed have been under 25 yards, and it's my opinion that too much choke can actually be as much a liability as an asset, causing about as many up-close misses as long-range kills.
If I were using any double gun with choke tubes, would like the idea of one being an extra-full and the other being a modified.
But if I were buying a new turkey gun, I'd recommend an automatic for several reasons:
1) One barrel is less noticable than a pair of barrels to a turkey.
2) Automatics are inherently less "noisy" to carry than pumps. Pump actions seem to have a "rattle" from the action shifting a bit while carrying/walking. I've seen people spook turkeys with that noise.
3) Automatics have the least recoil. Maybe not a big deal, but a noticeable difference when pattern testing.
4) Less options to mount an optical sight on a double gun. This would be my main reason for not going with a double gun as a turkey gun.
5) SHOULD you need follow up shot(s), nice to have a magazine with 3 extra rounds compared to just one with a double gun.
If we limit ourselves to high-probability shots, seldom should a 2nd shot be needed. But just in case, I do have my automatic loaded with progressively larger shot for each subsequent round. Typically, my chambered load is #7, as I only go for head shots, else don't take that initial shot. The next chambered load is #6, the next is #5, and all my turkey shells are now any of the heavier-than-lead types.