It has been my experience that the typical 835 which has a over bored (back bored, whatever you choose to call it) barrel will out pattern the typical 870 when it comes to turkey loads. There are of course exceptions to every rule but that has been the rule in my experience. And I speak as someone who owns both.
The best pattern I have ever gotten a 870 to throw at 40 yards was about 190 pellets inside 10 inches at 40 yards. A great killing pattern to be sure. But that was after trying many combinations of chokes and shells before finally deep polishing the inside of the barrel, adding a 100 dollar custom ordered Rhino choke and using custom order 8 dollar apiece Nitro Ammo Company shells.
On the other hand my 835 with an over the counter Hevi-Shot choke and over the counter Hevi 13 ammo will put 270 + inside 10 inches at 40 yards.