If you have lower impedance, difference can be like you loose attack.
I`m noticed such situation when compared direct guitar (with passive pickups) recording though screamer into amp (screamer has around 500k input impedance) to reamped signal (recorded though instrument preamp with 1M). Can post such samples.
Of course, active pickups works almost with any input impedance (difference in level and slight difference in ultra low end response, see charts).
500k (or so) input impedance is suitable to mimic screamer input impedance, 1 M mimics usual tube amp input impedance.