a considerable difference
The two approaches intuitively feel different, but they are not - The result is the same when you consider them objectively; The engine is producing minimal or zero power, because one of the necessities for combustion has been substantially reduced or removed. The engine continues rotating, and the restoration of sufficient air, fuel and spark will see it accelerate to normal speed.
the engine ... will return to full power on application of the throttle.
Anyone who believes that statement as a certainty, and operates aircraft that way, will eventually find out just how hard an aircraft can bite, unfortunately.
If you use the throttle to simulate the failure, a tired throttle accelerator pump may allow the engine to stumble when you push the throttle open, or very low power settings on a running engine may allow plug fouling. Where's the full power at a critical moment now ? Neither of those problems would have occurred if the mixture had been used to simulate engine failure.
There is no perfect answer, but we need more light and less heat in the discussion. Here's a couple of quotes from Lycoming. I suggest reading the whole article.(
http://www.lycoming.textron.com/supp...Operations.pdf)
Big radial piston engines with short, stubby crankshafts could tolerate the abrupt technique. However, flat-opposed piston engines with their long crankshafts and attached counterweights could not as readily take the abuse of suddenly snapping a throttle shut, particularly at takeoff or climb power. Use of the latter technique would tend to detune crankshaft counterweights and could possibly result in a nasty engine failure.
...
Since it was common technique by flight instructors to terminate power abruptly to simulate an engine power loss, we had to protect the engine. As a result, we published in our Engine Operator’s Manual and in Service Bulletin No. 245, the recommendation that if the power was abruptly terminated, it must be accomplished with the mixture control. Of course, this was intended for the higher altitudes where a complete engine shut-down could be conducted safely.
...
In our publications, we then explained the reason for using the mixture to abruptly terminate power. By putting the mixture control in idle cutoff position with the throttle in a normal open or operating position, the pilot merely cut off the fuel, but allowed the air to continue to fill the cylinders with resulting normal compression forces that are sufficient to cushion the deceleration of the engine and prevent the detuning of the crankshaft counterweights.
However, any practice of simulated engine-out condition at low altitudes should be best accomplished by a slow retardation of the throttle in accordance with the NTSB recommendation.
Lastly, there are important instructional principles involved in using mixture rather than throttle to simulate the failure. When I slide a map between throttle and mixture levers, I'm signalling that this is a practice engine failure; The student doesn't know when the failure will occur or which engine it will be, and they get normal cues about the engine failing. Nothing has changed in what they are required to do, or when, or what should trigger their actions. If I use throttle, they immediately know exactly what's happened, but even more importantly, they know it from non-normal cues - The gear warning horn and the throttle lever position. I've taught them a falsehood.
In accordance with the Lycoming and NTSB documents, I do use smooth throttle retardation where appropriate, but I rarely practice asymmetric engine failures at heights where that is applicable anyway.