EPR is the measure of a quantity that relates to the performance of the engine.
N1 relates to a parameter which is responsible for the performance of the engine.
As such, N1 does not take into account the other variables which may affect thrust, such as engine performance degradation after several years. If, for example, 50,000lbs of thrust demanded a hypothetical EPR of 1.27, no matter what the status of the engine, an EPR of 1.27 in the same atmospheric conditions is guaranteed to deliver the same amount of thrust. However, if this thrust required around 90%N1, and the engine gradually degraded over time (time period being many months or years), the N1 required to deliver the same thrust in the same environmental conditions will now be higher.
In this way, N1 is not a reliable parameter for thrust setting over very long periods of time, while it is the presence of an N1 indication that enables crew to recognize performance degradation. Consider an engine suffering a bird strike. Blades will get damaged, due to which the pressures developed across the engine will suffer. If at that point, the N1 and N2 are held constant, the EPR may fall below the otherwise expected EPR. This way, the crew can ascertain that the engine has been damaged. By the extent of deviation of EPR from the expected EPR at the given speeds of N1 and N2, the extent of damage may be gauged.
Under such a condition, advancing the thrust/throttle levers till the EPR value is close to the desired values will ensure almost the same engine thrust, albeit at higher engine rotational speeds. A display with N values only will not be able to convey as much information to the pilot.
N readings, if not the primary readings in certain engine-aircraft combinations, are definitely a lot more reliable due to their independence from other measured parameters. The EPR on the other hand needs carefully positioned probes, which must provide both pressure and temperature data to a computer (without temperature data, thrust is not controlled in the EPR mode but the N1 “unrated” mode).
This EPR control depends upon two probes providing minimum 4 data, in contrast to the N sensor which needs only rotational speed data from a single sensor. In case of an inability to control thrust using EPR, the thrust control system always falls back upon a more reliable N1. In fact, when setting thrust, crews always cross check the developed EPR with the engine N1. In effect, this increases crew workload.
While N readings are not true indicators of thrust, an undamaged engine over a substantially long period of time will hold a good correlation between generated thrust and N readings in known atmospheric conditions. EPR may provide the crew with better awareness about the engine performance, but the EPR itself is nowhere as reliable as the robust, independent and highly reliable N readings.