Regor,
I cannot claim to have more than the vaguest idea of which method is used in this or that engine, so I won't enter the debate above.
But if we can get back to the original question, we can try to answer it by looking at what the two methods consist of and what their use (implicitly) assumes.
N1 is a measure of the RPM of the low pressure spool, which on a turbofan engine includes the fan. In modern turbofans, the fan produces the majority of the thrust at low airspeeds, so it is reasonable to expect that N1 will give a reasonable indication of thrust.
But as an individual engine gets older the efficiency of its various components degrades, The fan and compressor become dirty eroded and in some cases corroded. These processes reduce the efficiency of the fan and compressor, thereby reducing the thrust produced at any given N1. This means that the accuracy of N1 as an indication of thrust gradually decreases as the engine gets older. Using the same N1 throughout the life of an engine, will cause a gradually reduction in the amount of thrust being generated. So N1 is accurate when an engine is new, but becomes less accurate as it gets older.
EPR in a non-bypass engine is the ratio of the low pressure turbine outlet pressure to the low pressure compressor inlet pressure. The low pressure turbine is the last in the series and the low pressure compressor is the first in the series, so EPR is a measure of the pressure increase produced by the engine. This increased pressure is used to accelerate the air through the propelling nozzle in order to produce thrust, so EPR is a pretty good measure of thrust.
Although the gradual reduction in component efficiency referred to above, also affects engines using EPR gauges, this does not have any significant effect on the thrust generated at any given EPR. So the accuracy of EPR as a measure of thrust remains almost constant throughout the life of an engine.
The gradual reduction in component efficiency does however mean that ever-greater RPMs and turbine temperatures are required to generate a given EPR. So if we were to use the same EPR setting throughout the life of an engine, we would eventually exceed the RPM or turbine temperature limits. In reality of course we monitor these gradual changes and replace components before specifed degradation levels are exceeded.
As stated in previous posts, the use of EPR measuring systems in high by-pass engines is a bit more complicated because it has to take accoiunt of the effects of the separate hot and cold gas streams.
At the end of the day, both N1 and EPR can be used as indicators of thrust, provided the other relevant parameters such as turbine temperature are also monitored. If excessive temperatures at any given N1 or excessive RPMs or temperatures at any given EPR are ignored, it really doesn't matter what type of thrust indication system is used. Engine life will be dramatically reduced!