If the compass readings are accurate and its 3 axes are perfectly orthogonal to each other, the vector sum of 3 compass readings (x,y,z) should be very close to the MFAM reading, assuming the local gradient is small. However, due to two main reasons, very often customers find a big difference between the vector sum and the MFAM reading.
1. The compass inside the MFAM driver box is NOT a top-rated vector magnetometer, in terms of reading accuracy and axis orthogonality. A top-rated vector magnetometer, capable of producing good vector sum readings, costs thousands of dollars and is much bigger in size.
2. The compass is integrated on the MFAM driver board, which has many magnetic components. The magnetic field at the compass location is altered by these magnetic components.
Although the compass doesn't generate good absolute readings, its relative angle measurement (related to the reading repeatability) is good enough to be used for maneuver noise (heading effect) compensation.