I've only ever used them with Zwift, and the differences I mentioned were noticeable when doing a workout on ERG mode.
But each turbo was the power source and not using a Stages or other external source for reading power? It could be that the Flux overread and the Kickr underreads or it could be the delivery/feel or a bit of both.
I haven't used any other device for power readings, only ever the turbo itself. I think a lot of it is feel. I find that the flywheel speed has more of an influence on the Kickr, like I need to be in a heavier gear to avoid the ERG spiral of death.
But each turbo was the power source and not using a Stages or other external source for reading power? It could be that the Flux overread and the Kickr underreads or it could be the delivery/feel or a bit of both.