I live in NW Iowa and was shooting pheasants quite awhile before I had a drivers license. I've shot them with all the presently available gauges and even the .410 to prove I could though it is not a shotgun to use on pheasants.
There is pheasant hunting and then pheasant hunting. Over a dog in thick cover I often use a little AyA 28 ga. with 3/4 oz of 6s or 71/2s - the "square load"; that is, a load of shot as tall as it is wide, the load that makes the 28 seems to kill "bigger" than it is. The square load lessens the shot string length and has few deformed pellets - flyers - on the periphery which negates the better pattern expected with more shot. The pattern may look denser on a two dimensional pattern board with a 3" magnum in a 20 but add the dimension of length and now you have a longer shot string with fewer pellets hitting the target at the same time. A 20 ga. is also excellent over a pointed dog but stick with the better balanced 2 and 3/4 oz loads and don't go too big in shot size, perhaps not bigger than 6s or 5s at the outside.
The square load is about 7/8 0z or practically 1 oz in the 20 ga., near 1 and 1/8 in the 16 and close to 1 and 1/4 oz in the 12.
When you are pushing wild pheasants in row crops you will get roosters running (the fact that their is a path or row seems to make them run quicker than some wild, thick grass patch) and then flushing at 3o yds. and out. Then, you can go to the bigger gauges but keep your loads balanced and of good quality. Generally, the smaller the gauge the better you'll be with smaller shot all other things being equal.
My advice is to carry the 20 with good loads of 1 oz to the short mag if you want of 1 and 1/8 0z of 6s. There are so many birds in S.D. hold up on the 40 yarders and take the sure-thing- shots of 35 yds and in.
