A narrowband is what you get from the factory. A narrow band O2 sensor is only accurate at the stoich ratio, 14.7:1. It's function is limited to reporting if you are above stoich or below stoich, allowing the computer to run the engine in closed loop and maintain 14.7:1. It will NOT accurately read anything other than stoich! (14.7:1). The output is normally 0-1.0 volts. If you do try to use this sensor for tuning anything other than stoich, you will constantly get false and confusing readings, likely causing the tune to be completely off. It is very temperature dependent, and as you are making the pull the voltage output will actually change, even if the AF is the same. Seriously, you can't use one for tuning.
A wideband is the only way to measure the actual air fuel ratio. They are a bit more expensive, but required if you want to see the AF ratio. The typical output can vary between 0-4.0 volts, but it depends on the type of sensor as I recall.
For tuning, the only way to go it wideband. if you buy a narrowband, all your getting is a lightshow straight out of fast and the furious. For people like me that use tuning software to make their own tunes, your car lives and dies by accuracy. and for that, a wideband is the only way.