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Stock prop is flexible but the carbon one is super stiff thus gives different reaction to the GAIN setting. It depends on several factors (prop size and pitch, total flying weight, wind, etc), you will have to experiment on the gain setting. The stiff prop is much more sensitive to the balancing act by varying the speed of each motors, the carbon prop has more (quicker) respond so much so that the correction is over compensated and as a result produces the oscillation effects. This is similar to the coreless servo or digital servo for the rc helicopter rudder that needs to reduce the gyro setting otherwise the helicopter will oscillate or "fish tailing".
You can set the gain for the stock props up to 180% with no oscillation, try it and you will see.