I think it has been summed up pretty well. I've always looked at it as EPR shows engine thrust output while N1 shows only engine rotation.
It could be argued that EPR is harder to use, which is understandable being that engine thrust is not linear with thrust lever movement and the cockpit EPR presentation isn't very user friendly. Wether EPR or N1 is used, at low thrust settings large thrust lever movement is needed to accomplish significant thrust (or speed) changes. At high thrust settings, small thrust lever movement results in higher thrust (or speed) changes.
The nice thing about EPR is that on TO it shows you the thrust your engine is producing (assuming the indicator is working propperly or there is no ice build-up). The N1 shows the fan's rotational speed (Kind off like measuring speed in a one-gear car by referencing the tachometer). The only problem arises in that if there is an abnormality like fod damage to fan blades, you might still show a normal N1 indication even though your engine might not be producing the required thrust (due to damaged blades).
So what is the solution? I believe one of the "big two" manufactirers has come up with it. I can't recal whcih one, but I read somewhere that the new A380 (maybe the 7E7) will have a percent thrust indication in the cockpit. This will be a computed value from 0 to 100% by referencing various engine sensors. So, it will be easier to read than EPR but offer the simplicity of N1. Its also more linear so it will be easier to match with thrust lever movement. For example; idle might be 5%, approach around 25%, cruise around 80%, and TO around 90 to 100%. This will be the same regardless of engine model flown, allowing operators more flexibility in powerplant selection (ex; two different engine models on the same airframe!).
Isn't technology great! Maybe I'll think differently when they find a way to get rid of me
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