It is more complex than you realize. If the strain gauge measures torque during the spool-up, then it must read the torque at almost exactly the same times as the RPM is measured in order to calculate the instantaneous power at each data point. Coordinating the simultaneous measurement of both RPM and torque is much more difficult than simply calculating the torque from the exact same data points used for the RPM calculation, where the data is intrinsically simultaneous.

Another big problem with the strain gauge is its frequency response. It needs to be free of mechanical resonances (which is problematic, since it is a spring!), and the bridge amplifier must have sufficient frequency response to make negligible the settling time to a value within the required error band.

Given all of the above, I'd say the strain gauge will likely be less accurate (and certainly less repeatable) than calculating torque from acceleration. Calibrating the calculated result to any given units might be more bothersome. But, as Mr. Phaneuf stated, that step isn't necessary to tune a motor, or compare motors.

It seems simple to me, since I have already done it. There is virtually no hardware required: the motor's existing Hall sensors, and one counter inside a microprocessor. Every other way of doing it seems more complicated.