Mag, I hope you're not inferring that a narrowband oxygen sensor somehow converts temperature into an A/F ratio...
Basically, the difference is that a narrowband sensor is calibrated at a single air/fuel ratio -- in most automotive cases it's 14.7:1. It can measure other air/fuel ratios, but only by calculating the rate at which deviations from stoich are occuring. 1.00v for 0% deviation from 14.7:1, and 0.00v for 100% deviation from stoich. That's part of the reason why the O2's cycle -- it's constantly finding its "limits" so that it can measure deviation with respect to another parameter. I know that sounds complicated, but a narrowband sensor is kinda complicated.
A wideband basically is calibrated at many points, and that data is stored in a computer. In 95red3000gt's case, the computer is the gameboy-looking LM1. But it is just as sensitive to changes in temperature as the narrowband sensors. It's just that oftentimes, you have a computer that's able to compensate for deviations from the calibrated temperature. Also why many widebands have a heater -- they are accurate within a very narrow temperature range -- they aren't any different in that sense than the narrowbands. Also, to put it another way, our O2 sensors are basically a primitive gas chromatograph that's calibrated to measure oxygen content, allowing us to compare what we put into the engine with what comes out of the engine.
Overall, a logger is mandatory. Somewhat-accurate narrowband logs are more valuable than instantaneous narrowband readings from a gauge. Once you've done the best you can with your narrowband tune, spend the money on a wideband. But either way, some sort of logger is mandatory.
- Dmitry