Hall sensors output is ratiometric, if supply voltage varies so will output.
This can be canceled (nearly) by powering the ADC and Hall sensor from the same supply.
Hall sensor zero is half it's Vcc.
Important to have Hall and ADC on same supply, any supply change will be canceled.
if not same Vcc any difference will be seen as offset changing along with gain change.
I could go on but you catch the drift! Pun intended.
Rshunt has it own problems:
The Gain and offset of the Rshunt and amplifier must be calibrated out. The amplifier and ADC must be on same supply or have problems similar to Hall sensor. Temperature and voltage changes.
Resistors of the amplifier need to be matching type to temperature cancel.
Rshunt connections are another set of problems, wire to spade connector to terminal port on shunt. Must be kept clean, and sealed from weather. Over time the crimp or spade gets corroded, resistance goes up creating a fault in the wiring. Another set of wires going to Amplifier, often must be shielded kept short as possible etc.
With attention to details both methods work. Hall fewer less connections and less resistance in the wiring and is Isolated from the battery. Some believe Rshunt are more accurate. Allelectronics shunt is 0.5%, 4x better than Hall, yet after calibration should be the same. Most resisters have temperature coefficient, not listed on the shunts. To build the amplifier requires 1% resistors to stay within couple percent error, calibrated out yet how about over temperature? Rshunt grounds and supplies are now connected, definitely a place for problems.
Have fun,
Scott Beversdorf.