Portability is the biggest difference for me. The Fitbit is small and can be clipped just about anywhere, or placed in your pocket unobtrusively. I don't carry my iPhone on my person 24/7, especially when I'm at home, and that to me is a big negative in maintaining consistent tracking. The downside to the Fitbit is that it's SO small that you can easily forget it's in your pocket when you change clothes. I can, however, testify to its ability to withstand several inadvertent machine washes and keep on keepin' on. Another plus is that it will carry a charge for up to two weeks.
I've had both the iPhone Health app and the Fitbit engaged for several hikes, and they generally agree on data. Generally. The Fitbit seems to be more accurate in measuring gain, displayed as "floors", when compared to known topo elevation. The largest discrepancy seems to be in calories burned, which is a crapshoot data point anyway and not one I'm overly concerned with.
