If you use multiple Nike+ devices, you may receive different NikeFuel amounts on each device for the same workout. That's because each Nike+ device uses different technologies and are optimized for different experiences.
For example, the Nike+ Run Club app is optimized for pace and distance and is the best device for measuring those metrics if you are a runner or walker, while the Nike+ FuelBand or FuelBand SE is optimized to capture your everyday activity as NikeFuel and is the best option for measuring your overall athletic life.
Feel free to use apps and devices at the same time if you're interested in both your sport-specific workout data and your overall activity data. Some variation between the two is to be expected and should not be cause for concern.