Both methods can have their downsides in the wrong circumstances. However for me the mixture method is the best way for two main reasons.
The RPM and manifold pressures guage indications realistically match a real engine failure.
The process of opening the throttle to verify the dead engine also acts in the same manner as it would on a real failure.
The student sees and experiences actions that very closely mimic a real failure which cannot happen by closing the throttle.
The situation described above re flying the windmilling prop to the ground then doing a touch and go is very risky by leaving it to the last minute to see if the engine will respond whether or not it's done with the throttle or mixture and is taking a scenario too far IMO.