Concentrating on referenced metrics (i.e. compare A with B) it might be nice, not to be forced to write a third image, but to get the measurement result for other purposes. This both is not possible at this time or I stood on my own feet.
This works & pipes the output of the "-list filter" option to a text-file
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convert -list filter >file.txt
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compare -verbose -metric PSNR IMAGE-A IMAGE-B IMAGE-C >file.txt

Best regards,
rengel