There has been some pretty hot debate about this. I feed my ducks game bird feed. My logic is that, if they were wild ducks, a good percentage of their diet would be protein from insects, fish and small amphibians. Even the aquatic plants ducks snack on are high in protein (like duck weed).
The wild cousins of your chickens eat lizards, snakes, frogs, bugs, etc... along with fresh greens.
If your goal is to feed your flock as cheaply as possible, extra protein is seen as an unnecessary expense. (This would be especially true for meat birds)
If you want to keep your hens at optimum health and simulate their natural, evolutionary diet as closely as possible, the higher protein is your best bet. This will also prevent health problems if you expect to hold on to your birds for a long time.