Probably the most accurate system, assuming it's well maintained, is R-R's integrated EPR. As the engine deteriorates with time, core thrust goes up, and fan thrust goes down. so the IEPR averages the two and stays closely matched to true thrust.
Not so with P&W's EPR, which measures only core EPR. Deterioration will drive up core thrust and EPR, which means that the decrease in fan thrust is not accounted for.
Since engine inlet total pressure is the denominator in EPR computation, icing or other blockage of the inlet probe can cause erroneous readings. This was a primary cause of the Jan. 1982 DCA
AF90 accident.
N1 is not susceptible to icing, and as described in the Engine Insight link, tends to be conservative when engine deterioration is considered.