N1 V/S EPR hve been a conflict between engine manufacturers and operators for years.
None the less there is a small variance between the importance of the two in respect to rated thrust.
High and hot elevations limit performance to MAX EGT limitations in most cases...In simple terms the ambiant temperature and environmental air pressure being the limiting factor.
N1 is limited to a fixed speed (should not exceed) and thrust is the calculated variable based on EGT limitations.
More importantly "hot" reduces the wings lift capability (less dense lift producing air under the wings). Having said this Sea level and hot can affect MGW limitations for takeoff at sea level as well.
Runway length becomes the most prohibitive factor as well as terrain for alot of operators trying to get off the ground in hot thin air. The heavyweight freight operators are affected most.