Car Tech: oxygen sensor function, upstream and downstream

oxygen sensor function, upstream and downstream

I have a 1997 Jeep GC Ltd 4WD 4.0L that has two oxygen sensors, one upstream and one downstream. It's setting a code 51 that my Haynes manual explains in two related, but significantly (I think) different ways.

Explanation 1: Oxygen sensor signal input indicates lean fuel/air ratio condition during engine operation.
Explanation 2: A lean air/fuel mixture has been indicated by an abnormally rich correction factor.

The first seems to point to a faulty O2 sensor, but which one, the upstream or the downstream sensor? Clue: engine runs rich in open-loop mode (engine cold). Does one of the O2 sensors send a signal to the ECM when the engine is cold? If so, which one? First guess would be the upstream sensor.

The second explanation may point to a faulty ECM that is over-correcting based on one sensor input or other, as well as a faulty O2 sensor. However, I replaced the ECM about a year ago with a Chrysler ECM, so that's not likely.

Bottom line is, I don't have a lot of $$ to spend on replacing parts that may not be faulty just to see if it works, yet I have to drive my Jeep ~ 50 mi/day for work. I haven't bene able to find any explanation about the operation of the upstream and downstream O2 sensors in open- or closed-loop modes.

Anyone help?
Thanks.