I haven't tried Alton Brown's recipe.
But brining has never given me anything less than spectacular results. For those who are reluctant to give it a try, the results aren't salty and the breast meat is incredibly moist and tasty. I served it to my Mom without telling her what I had done and she was simply amazed. When I later told her how unconventionally it was cooked, she could hardly believe it. She still "disapproves" of how my wife and I do our potatoes, yams, brussel sprouts and pumpkin pie, but even she has to admit to my turkey is pretty good.
But (and these are some big buts), no pan gravy and no in turkey stuffing. You also have to buy a fresh turkey. (Note: make gravy from the neck and giblets then use maybe a quarter cup of the pan juices for flavor. The results are great.)
Somebody else has already stated this, but you really don't need any herbs or vegetables. Salt and water is all it takes - I've tried the fancier versions and they make no difference whatsoever.