Sure, you should use high accel/decel and as high a speed as is practical.
Doesn't a "spike" in a position error graph indicate overshoot? That may not be what you are referring to (I'll wait for your pics), but that is not something you want to allow.
Do both motors have the same encoder resolution? I'm not sure of this, but I'm supposing that very high count encoders are used to give better control of the motor, not merely because we want to split hairs on positioning.
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