Both methods have their advantages, disadvantages and vulnerabilities (is that a word?) that can lead to the available thrust being lower than what might be expected from the indications.
One specific accident where N1 was of no use at all was the forced landing of OS111 (Fokker 70 OE-LFO) at Munich 2003. The
Accident report is available in German language only, as far as I know.
This flight had the bypass duct clogged up by improperly attached ice impact trays that came loose in extreme icing conditions and got stuck in front of the fan stators. High N1 values together with next to no EPR ensued, as nearly no noticeable thrust was produced any longer, although the engines were still running. While this may have been a freak accident, it still shows that N1 only indicates how fast the shaft is spinning, not how much thrust is actually resulting.
So with two imperfect methods of measurement, I would tend to prefer to get as much information as possible on the engines state. Observing the two power plants show not only equal EPRs but also symmetric, plausible N1 and other values is a better indication of everything being in order than only seeing the symmetric, plausible N1 and other indications.
It all boils down to philosophy though...