Marc Edwards tracked his step counts with both his iPhone 5s (using the M7 motion coprocessor) and his Fitbit Zip. I have to say, those results are pretty close.
I wear a Fitbit One every day to track my activity. I wonder if I will even need it with the iPhone whatever-they-call-it-next. (I'm not up for a new one until next fall). Presumably the M8(?) will be even better, and my iPhone is almost always with me.
I can see the one area I'd lose stats in is the Fitbit One tracks my sleep activity. I could go without it, but I have been able to determine when I am in a more active state of sleep in the morning by studying my sleep habits, and adjusting my alarm accordingly has resulted in a better me.