Typically, the EFIE is used for gasoline (petrol, Benzine) engines, or better, any 'ICE' (Internal Combustion Engine) that is not diesel that HAS oxygen sensors (lambdas) installed into the exhaust manifold of a vehicle. It usually includes almost ALL gasoline engines since about 2002 but CAN include some engines as far back as 1980s.
The MAP/MAF is typically used for diesel engines, where there is the use of a CPU related to fuel control. The MAP/MAF is used to help control fuel delivery on these diesel ICEs
That is the basic difference.
Some very new diesels (2011 and 2012) are being fitted with Oxygen sensors as well! This furthers the need for accurate monitoring of fuel for economic gains in consumption