John,
The EFIE (Electronic Fuel Injection Enhancer) is for the Oxygen Sensors is used to add voltage to the sensor signal therefor telling the ECM that the fuel mixture is rich.
I personally always said use a map enhancer because there is no other way to control the way that the ECM reads the vacuum and then try O2 extensions because is cheaper than the EFIEs, but sometimes there is no space for extensions then you will need to invest in EFIEs. You will need to control the before cat O2s (Upstream O2s) so if you have two sensors before the cat then you will need to EFIEs.
Anytime that you're tampering with any sensor and you get out of the sensor parameter the check engine light will come on.
I'm gonna write a small article about those two sensor to explain how they work and that will make you understand the principle behind these two enhancers better.