Two big negatives for me...one is the obvious, the corn cob effect gets more of my attention shooting than it should (I just plain hate the looks of the Polychoke and the Cutts); two, is the effect of lowering the point of impact of the gun. One could build up the comb to compensate...
The older I get, the less enamored I am of variable chokes, choke tubes and the like. I have several guns w/ choke tubes, use them, but find also that my fixed choke guns are not much of a disadvantage in their realm. For example, my plain Jane field Model 12 Winchester 16 gauge has a modified choke, about .012" constriction, and I really can't remember feeling I needed something much different (it's my favorite chukar gun, and has done some fancy work on sage grouse as well). My 12 gauge Model 12, with fixed full choke, is a tremendous dove gun when they are high and fast, and wouldn't be helped with less choke. For close stuff, it's simply too heavy and long to be ideal, so full choke is perfect.
Another point worth mentioning, much like with variable scopes, is the temptation to be twisting the choke and thinking about it too much at the expense of focus on more important things (like the bird, dog, etc.).
Not disparaging those who like them, but the variable chokes don't suit me.
