Hmmm, let me try this one;
All modern engines use an oxygen sensor to determine where the after-combustion is stoichiometrically (is this a word?) The purpose of the ECU is to pre-determine the correct air-fuel ratio by its fuel mapping with the O2 sensor filling in the blanks and to allow for adaptive learn. You might say that the ECU provides about 90% of the fuel mapping with the O2 sensor the balance. That's why most vehicles run almost as well with the O2 sensor unplugged (albeit a little rich) and at extended idling and WOT too. In these conditions, the O2 sensor values are out of range for effective ECU block-learning.
NOx is the highest at stoich, lower at rich and very lean mixtures. HC's will show up at the O2 sensor as insufficient O2 after combustion. The purpose of the second O2 sensor (post cat) is to determine catalyst efficiency, by comparing the pre and post O2 sensor signals. A rear O2 sensor that mimics the front sensor means that the cat is no longer effective.
Other variations on the O2 sensor is the wide-range or UEGO sensor that actually produces a linear signal versus the rich-lean knuckle sensor so widely used. The linear UEGO is beneficial when operating an engine in ultra lean regions where the knuckle sensor is ineffective.
DISI engines are fighting the cold engine excessive HC's (soot) problem know. Particulate trap type cats are pretty effective, but the secret will be to eliminate the wall wetting effective on a cold engine (gaseous fuels do not have this problem with DISI).
Franz