Midlife flyer is right - both mantras are training techniques. The ultimate pilot must learn that the coordinated use of pitch and power must be mastered to accomplish control of altitude and airspeed.
HOWEVER...having said that, MOST people cannot wrap their minds and hands around that concept at first, so, in keeping with good training technique, you break it down into a manageble task. I teach the mantra of "Power to airspeed, Pitch to altitude" right away, right from the first day.
"See the nose going down?...pull back a little on the yoke/stick...see the nose going up?...push forward a little on the yoke/stick."....Don't you do that? I do. Pitching to the altitude all the way.
"See how we are descending to low on final?...pull up a little...see how that makes the airspeed go down?...add a little power."
I know some die-hards will scream that the student will pitch up without adding power on final and get too slow. That is why the opposite mantra exists. But I have been practicing the pitch to altitude approach with new students for many, many years now, and never have had a student pitch up without adding appropriate power. And then later when he starts instrument training, I don't have to break him of the ingrained habit of pitching up off of the glideslope when the airspeed jumps up due to turbulance. "Elevator to the glideslope, and throttle to the airspeed." Yep.