I would imagine like most others I use the method that my instructor was taught and his instructor was taught. There is a big debate still going on discussing which method is better with neither side really giving into the other side.

Half way through my private pilot training I switched instructors with the first tecahing that power controls altitude and the second teaching that power controls airspeed. It set my flying back a little bit as I had to relearn some things the other way.

With that said, I think it is a combination of the two methods that work the best. For example, if you want to climb quickly at cruise flight, pulling back on the yoke will cause you to climb. Power won't work as there isn't enough power to spare to climb without lifting the nose. If you want to descend, you can always pull power all the way to idle and you will indeed descend albeit in a stalled condition perhaps.

If you want to go faster at cruise, it doesn't make sense to lower the nose (thus descending) without adding power. If you want to go slower, it makes sense to pull power and pull back on the yoke to keep your altitude.

Both sides of the argument agree that it's a combination but what they disagree on is what is the primary factor for both. If power controls airspeed and you want to slow down, this pilot will pull power first and then realizing a descent pull back on the controls. The other pilot will first pitch up to slow down and then realizing they are climbing will pull power. The end result is the same (same flight attitude and power setting) just different roads on how to get there.

I think the biggest difference is in how the two groups of pilots land the airplane. The group that says power controls airspeed will point the nose towards the runway and pull power to reduce airspeed. The power controls altitude group will have a higher flight attitude with power controlling the descent rate.

Having flown both methods, I think that power controls airspeed and pitch controls altitude is the better method in the specific case of landings. It seems to be more stable with the lower flight attitude and I can see better where I want to land the airplane. (This was the second instructor who taught me).

I hope this gives you a understanding of my thought process.

It's a bit more complicated than that. Controls are seldom operated one at a time.

If you are using pitch to keep speed constant, then power controls vertical speed and thus altitude. If you are using pitch to keep a constant altitude, power controls speed.

At constant power, pitch will increase climb rate, at the expense of speed, or increase speed at the expense of climb.

On approach, you can control flight path with pitch and airspeed with throttle, or you can control airspeed with pitch and flight path with throttle.

With a dead engine, pitch controls both, but as in the case of constant power (which this is - zero), there is a trade-off. You can increase the glide (land longer) by adjusting airspeed closer to best-glide speed, or decrease the glide (land shorter) by deviating from best-glide speed. Deviating too far too soon can put you at stall some distance above the runway, or put you at runway height with too much speed to land. Rudder can also be used to reduce the L/D ratio to increase sink rate, controlling altitude.

In a glider you have no throttle. Pull up to go up, push down to go down. It also is good to know that there are other effects to manipulating the controls...

Throttle controls the engine which will produce more thrust when power is added. Thus more forward speed.

EDIT

Try to take off using the control stick to get speed. It doesn't work. You need the throttle.

Autopilot units are programmed to use power for airspeed and pitch for altitude.