
Impedance missmatch would result in a muddy dull sound and some decrease in level.
Best example a shure SM57 (500 Ohm AFAIR) on a bad mic preamp.
You don't tell what mics exatly but I guess both are condensors. Those have low output impedance, so even a bad mic preamp shouldn't have impedance problems.
Make sure it's not one of the trivial ones: demaged cable, missing phantom power, wrong wiring.
P.S. I couldn't find a speck, where input impedance of he bmpcc is mentioned ... ;-(