Ah yes! The old "pitch for airspeed, power for altitude" theory. Or "pitch for altitude, power for airspeed".
Note: in the older days we said "pitch for airspeed, power for RATE"
Having flown for the last 30+ years, in big one's and little one's, fast one's and slow one's and still going today, in real flying you use a bit of both.
Look at it this way, if the autopilot is on and it has auto throttles and its following the flight director, then it will pitch for altitude, power for airspeed.
Another way to look at it is. If power is fixed "no power glide" you pitch for airspeed.
It also depends if you are flying straight wing or sweep wing.
Small straight wing aircraft "Piper, Cessna etc" where there is limited power you pitch for airspeed in climb and get whatever rate you get. This can also apply to sweep wing aircraft in the climb to a certain extent, speed limits below 10,000 in the US. Where you would fly pitch "X" and power for airspeed.
You normally don't see small training aircraft or for that matter prop driven aircraft with AOA indicators.
As for landings in sweep wing aircraft, yes we normally fly on speed AOA, but you also control the path with pitch, meaning in the REAL WORLD you have ever changing atmospheric conditions. In other words the aircraft is not on a rail.
So in the real world of flying you just don't think about it to hard.
As my instructor told me, "Just fly the f#%&^&* airplane and don't worry about IT!
:doh: