A wideband o2 sensor system will give you far greater tuning ability than a narrowband sensor. The problem with a narrowband sensor is that it is only truly accurate at 14.7:1 AFR. The factory will have tuned your engine to run around at 14.7:1 air/fuel ratio (AFR) at cruise and light load conditions. This is the ‘chemically correct’ or ‘stoicheometric’ (stoich for short) AFR which basically means this is the air/fuel mixture at which the most complete burn of the fuel will occur. It happens to also be the proper mixture for the catalytic converter to best do it’s job. In other words, you car comes tuned from the factory for reduced emissions and that’s why that narrowband sensor is there. Therefore it will be useful for tuning cruise Air/Fuel Ratio (AFR) only as long as you’re tuning for 14.7:1 air/fuel ratio. However, under Wide Open Throttle (WOT) you’ll want to tune for somewhere between 12.6:1 and 13:1 (NA) or richer for forced induction, and the narrowband won’t tell you anything useful at that range. Likewise at cruise you may not want to tune for 14.7:1, maybe you want better fuel economy at cruise and you want to tune to 15.5:1 or even a bit leaner possibly. Only a wideband can give you accurate feedback outside of the stoichiometric 14.7:1 reading that NB sensors are designed for, and allow you to tune for best power and best economy.
In short, a wideband oxygen sensor will give you a measurement of your Air/Fuel Ratio from about 10:1 up to about 20:1 AFR allowing you to target exactly the AFR you’re after at all times. A narrowband can only tell you when it’s 14.7:1, and is therefore nearly useless for tuning.