Both techniques are applicable and most of the time you will be using them both without knowing it. In a classic airspeed case, whether climb, level or descent, you will hold and set speed with attitude (elevator). You will use power as a constant (climb power for climb, cruise power for cruise etc). Remember POWER + ATTITUDE = PERFORMANCE?
On approach, you will use the classic technique during the initial base and final until you have a more important parameter to control, that of the glide slope. The glide slope might be a VASIS, an ILS GS, or a visual glide slope based on what you are seeing out front.
Once on the glide slope, it makes more sense to use the elevator to stay there. A little speed excursion is not as important as remaining on the glide. If the airspeed is within a reasonable tolerance leave the power alone. Usually the speed has changed as a result of the airplane going above or below the glide, so if you simply return to the glide slope the airspeed will recover nicely all on its own. If the airspeed is consistently high or low, make a power adjustment while you continue to control the glide with elevator and all will come right.
A jet airplane will mostly use this technique, since an accurate glide slope is vital. An auto throttle is keyed to speed, not to approach angle, for this reason. However any airplane can be flown this way and it will result in more accurate landings.