The reason these techniques exist: You can't just say to a new student, "do this and this and this", as they won't know what it is they are trying to do. So, these methods are invented to try and make sense out of the initial mystery of flying an approach.
As a pilot gains experience, he/she may combine the two techniques, and fly a mish-mash of the two, without actually knowing what it is that they are doing. All they know is they can fly a safe approach, at a set speed without too much thought.
Do the two actions of elevator/throttle at the same time, and the two techniques mostly become one and the same anyway. For a pilot new to training, they won't know this, as there are too many variables for it to make sense to them, so it needs to be broken down into a technique they can use.
However I may need to learn the other commonly used technique of power controls RoD, Elevator controls Speed.
What you
really need, is a good understanding of how angle of attack (alpha) works, and how it is alpha that you adjust with the elevator. (Read 'Stick and Rudder'
)
Imagine starting a descent in a light single engine aeroplane (The usual, inherently stable training type like a PA28/C172). You set the power somewhere around 1800rpm and trim for 80kts say. So, hands-off, the aeroplane will happily descend at 80kts, because (whether you realised it or not) you have set an alpha at which the wing is maintaining 80kts. You are trimmed for 80kts, and the aeroplane will be in a steady state, where it will want to fly at 80kts no matter what you do with the throttle. Or, if you were to pitch up momentarily, and bleed the speed back 5 or so knots, then release the controls, the aeroplane would want to return to it's trimmed speed and the alpha required to fly at 80kts.
So now, in your hands-off 80kts descent, reduce power to 1500rpm from 1800... As the power reduces, the nose will drop as the wing tries to regain the 80kts it wants. Essentially, you are now controlling your RoD with power. The elevator is used to set the pitch to which the aeroplane would go if left to it's own devices. Hands-off, it would control it's own pitch to return to it's trimmed alpha at a certain speed, would it not? But, instead of allowing the aeroplane to wallow about and hunt the alpha it wants for a set airspeed, you pitch the elevator to set the speed after you have adjusted the throttle. If you chopped the power, obviously you're gonna need to pitch down to maintain the airspeed, and hopefully you already realise this. That's all there is to the Power=RoD/Pitch=Speed method.
The major problem with teaching this technique, is that a student will then firmly believe, that airspeed is controlled first and foremost, with elevator. So, in a time of crisis (where airspeed suddenly drops on short final) they will try and pitch forward, shoving the nose down to try and regain airspeed. Obviously, not a good idea at low altitude.
Because I have used point and power my entire flying career I am finding it very difficult to understand how this technique works?
Go for a play and experiment at altitude. Start a descent, trim for an airspeed then play about with the power. After adjusting power, pitch as necessary to maintain the airspeed you had before you altered power. That's all there is to it.
It would seem to me that if you control your speed with attitude that you would end up undershooting or over shooting?
The point-power version of events you use would always seem more accurate, simply because you're always pointing towards the TDZ. (You would probably be surprised that your airspeed holding isn't that accurate with this method.) You would literally be pointing at it, then faffing with the power to get the airspeed you want.
Imagine you turn final and it becomes apparent that you're WAAAAY high. What would you do? Point/power would dictate you'd stuff the nose down, then as the airspeed increases, bring back the power. If, instinctively, you'd chop the power first, then that's a good example that you've already started developing more of a feel for things instead of just "flying by numbers" in a monkey see monkey do kind of way. I'd argue that both techniques drift into insignificance once you have 50 odd approaches under your belt, as you find a way that works for you without thinking about it too much. If you're still flying about post-PPL, worrying about whether power or pitch comes first, then I would question the quality of your flight instruction up to this point.
I personally favour teaching "power then pitch" - with the caveats regarding low alt and diving for airspeed. The demonstrations mentioned above would also be given prior to flying a proper approach. I try to avoid breaking it down into 2 areas after the initial couple of approaches if a student is progressing well, preferring that power/pitch are adjusted simultaneously.