Brings to mind the old country saying 'Are you going to believe me, or your lying ears.'
Hey, that's a good one. What country?
Hey, if you are running rich at 10:1, or lean at 20:1, my suspicion--just a wild hunch here--is that you don't need a [expensive and sophisticated] gauge to tell you. Just a guess here, though. The narrow band is a tool of the racing trade, working with installed o2 sensors; the wide band a diagnostic tool of high performance tuning.
If your car is good enough all around, with no vacuum or exhaust leaks, all electricals 100%, known and good engine condition, known and good fuel quality and all the other parameters that affect performance known and controlled, (and in our cars that includes things like performance of the FI system and injectors) and you want to tune your car for peak performance, well this is one tool to do it. (This is the reason why you see these devices used as precision tuning devices for high performance engines and racing--not a general tool of diagnostics. When you have a well running engine and car, they will help you tune it for peak performance.)
I'll let you know when I'm at that point.