Assume an ideal motor with no mechanical losses and
Operation in a perfect vacuum.
Call the two portions rotor and stator - with all attached parts such as controller and power pack forming part of one or the other.
Start at rest relative to a "fixed" frame of reference.
Rotor and stator will rotate in opposite directions with the 'momentum of each portion being equal and opposite. If you manage to produce identical moment of inertia in rotor and stator they will rotate with equal and opposite rotational velocities. In the moments of inertia are in the ratio N:1 they will accelerate and, and will rotate with velocities of 1:N relative to the fixed frame of reference. The energy content in rotor and stator relative to the zero energy level initially will be equal.
If there are non idealities such as bearing drag and eddy current or other losses they may affect rate of acceleration or final velocity depending on how the motor is controlled. A "brushless dc motor" whose speed is controlled by sensors or field sensing so that a fixed RPM rate is achieved will rotate so that differential rotor-stator speed is what the controller sets, and relative rotation rates relative to the fixed reference frame will relate to the relative moments of inertia as above. A motor such as a series wound "universal" motor whose speed is set only by losses (such as is typically used in vacuum cleaners) will increase in speed until losses from bearings, eddy current, copper losses etc equal power in. In such an environment an unloaded motor would usually easily accelerate to an immensely high speed and "self-dismantle". (Even everyday vacuum cleaner motors which depend on the aerodynamic loading of their fans will usually rev to destruction if operated without the fan.
For a rotational drive it is possible to introduce rotational realignment around the axis of rotation but not translation.
A motor with offset mass relative to the axis of rotation will do interesting things but still imparts equal and opposite inertial variations to the two parts.
If you now "add air" all bets are off - you can achieve arbitrary translation and velocity in desired (or undesired :-) ) directions because you have introduced an independent medium which reactive force can be developed against. You can also arrange energy losses differentially between the two portions so that eg a rotor could be spun up and the stator braked to rest while "floating".