My narrowband is right under my large readout wideband. (Powerdex/AFX)
From a "layperson" perspective, knowing that both are giving me "feedback" of some nature, the narrowband amounts to mostly a "light show" and the wideband is a much more functional tool that shows me the relative air-fuel ratio under various conditions in a much more accurate manner. The key appears to be not only to know the air-fuel you are achieving in any given state, but to further know what is the "target" within those states.
i.e.: If I am under full load on boost, I am wanting a RICHER tendency to be "safe", perhaps in the 10's or 11's, even though that's richer than stoich. When I am under deceleration or light load, I am more comfortable with a leaner mix in the 13's and 14's for example. (Not to mention these are references for GASOLINE, and different fuels operate optimally at different ratios...)
Cruising or idling, you often don't want to be too rich, as it's just blowing a lot of stinky into the air... and wasting fuel to boot, etc...
As I understand it, being in the 12's is often the power target, but as you can see above, it's not always the rule depending on your operating state and type of engine, boosted or non being distinctly different in what they "want" to see, hence needing differing settings, or targets. The wideband can help you monitor these specific ratios as a metric, and the narrowband is just giving you a "broad range" represented between, say, 11 and 13 as "STOICH" for example (there are specific values to what is considered "stoich"... perhaps another member can elaborate, as these are reference values for the concept as I understand it...) but such nb units are, as mentioned before, only accurate within the "LEAN/STOICH/RICH" ranges under CERTAIN STATES, such as FULL LOAD/WOT or IDLE. Not very helpful when it's mostly bouncing around the rest of the time.
I welcome any/all corrections, as I'd prefer to understand than defend my very limited understanding of this newly acquired and exercised set of instruments in the WB and NB. I am particularly interested in and fascinated by the subtle and complex relationships between especially the EGT (Exhaust Gas Temperature) gage readings and air-fuel monitor readings in varied conditions. Lots of stuff going on there when you start to play with ignition and cam timing, too.
-crisp