Out put torque measurements could be different as the, in put power minus the machine losses(friction windage+cooper loss+iron loss)), would be the output power, and would varies with ageing of machine.

If the torque meter is on the shaft between the electrical machine and the driven one, it is giving the actual mechanical torque

You don't have an instantaneous torque measure but an average or steady state measure generally.

Whereas the electrical absorbed power includes also the losses (eddy current, copper losses, in stator and rotor, and the mechanical losses_which are very low in comparaison_), you also need to measure speed to get the torque in this case. It is difficult to estimate precisely the torque with this mean because of the difficulty to compute the losses (Resistance changes in function of the temperature, eddy current in fonction of the voltage and operating point (magnetisation),...)

Hopkinson test would be giving the best value of losses of machin ...

Yes Hopkinson test conduction is also easy and straight forward to conduct in the laboratory