Great discussion here, took me a while to catch up after being away for a while.
First, I reckon it all ends up the same, it's just the way you think about it. Way I was taught, if I'm undershooting the aim point, I add power first to control altitude, then exert back pressure to maintain my approach speed. If I'm too fast, I exert back pressure to slow down, and reduce power to maintain glidepath. The alternative method does the same thing, except in reverse. On undershoot, pull back on stick to maintain altitude, add power to hold airspeed. If too fast, drop power to slow down, pull back to maintain altitude. Same thing.
But the mental process is quite different. I prefer the way I was trained because I reckon we need to think always about energy management. If we are too low (ie low potential energy) then the only sustainable way to increase our height is to add energy from the engine - the elevators just won't cut it (you can only trade off so much kinetic energy for height before you stall). So in the back of my mind, I'm always thinking that way.
The other day, I struck major sink on short final, nearly at the fence. So I applied a decent burst of power instinctively, as a result of my mindset. But to be honest I was shocked at the really strong temptation to just haul back on the stick with the ground coming up so close - I even commented to my instructor that I was surprised at how I almost had to fight it. Had I been taught the other way, my instinct might have been to go for the stick - not a lot of time to react or think, and not a good idea at low speed 50 feet off the ground!
I'm not sure about other schools, but at ours roughly 4 RAAus instructors teach power for altitude, and one t'other way. My instructor explained both to me, however.