The theory behind power chords is easy, you just take a major (or minor) chord and drop the 3rd.
Well, that's a bit like saying “making flatbread is easy: you just make a pizza and scrape off the tomatoes and cheese”. While it is possible to describe power chords this way (at least approximately), and can even explain quite well how they are used in some genres (in particular, rock that takes some elements from classical or just folk/pop harmony), I find it quite backwards to construct them this way.
See, thirds are not the basis of all harmony. In fact they are completely absent in some traditions, for instance Gregorian chant. When you start your theory from the Pythagorean scale, then everything is derived from fifths! A fifth is originally the interval between two notes whose frequency ratio is 3⁄2 = 1.5, which makes for a very natural, coherent combination. A major second (full tone) in that system is simply two fifths minus an octave, and a “major third” (ditone) is two such seconds stacked.
That leads to music where thirds are mere melodic intervals, with no direct harmonical relation. In fact they are considered dissonances in such old music! If you've ever played an instrument in Pythagorean tuning, you may understand why: those thirds (frequency ratio 81⁄64 ≈ 1.266) are jarringly wide.
Such music sure sounds quite different from what we're accustomed to today, but melodically it's actually quite similar, based on the same diatonic scales that still provide the majority of melodic material in western music.
In the Renaissance composers started to employ what would be considered our modern, consonant thirds: they discovered that if you make the thirds a bit narrower, you approach the frequency ratio 5⁄4 = 1.25, which also sounds very coherent. Using that interval in the middle of a fifth gives you a major chord. That's how it's derived, none of that “major third plus minor third” nonsense.
The scale you get when taking Pythagorean and lowering the major thirds is called Ptolemaic scale, aka just intonation. It's still a diatonic scale.
Now, after Renaissance came Baroque, and Baroque composers loved to modulate between different keys. That's tricky if your theory is entirely based on diatonic scales (a diatonic scale looks completely different depending on which note you start from), so alternative tuning systems were developed. Basically these always made some compromises in the quality of the idea consonant intervals, in order to at least allow some consonance everywhere you could modulate to. The ideal is a system where the scale looks the same from every point – a regular grid. In fact it is possible to approximate every step on the Ptolemaic scale to almost inaudible deviation if you simply divide the octave into 31 equal steps. That was proposed in the late 17th century, but unfortunately (IMO) never really caught on – those many steps, most of which don't belong to the key you're in at any time, make it hard to build an easily-playable instrument. Eventually a simpler system caught on: 12-edo, aka “the” equal temperament. That's sufficient to approximate Pythagorean fifths very well, but actually deviates quite notably from the Ptolemaic thirds.
But especially on “soft, plain” instruments like piano, these thirds still sound quite nice in chords, and people just got used to hearing them as consonant. Hence this tuning system became pretty much universal on keyboards and guitars.
Fast forward to the 1960s: enter distortion. Distortion has a tendency to make consonant sounds fatter and dissonant sounds more dissonant. Fifths are undoubtably consonant (or, pure), and the 12-edo approximation doesn't significantly change that. So playing a fifth through distortion sounds just great – you have a powerchord.
Major thirds do, in principle, also sound nice; in fact any low-integer ratio morphs into a fat, resonant unity if you play it through distortion.
However, the distortion makes even quite small deviations from just intonation very obvious. In particular, the 12-edo approximation of thirds comes out really not that satisfying anymore, in fact it's quite a mess of unharmonic components.
Upshot: distortion has made 12-edo thirds dissonances again. Hence it really doesn't make sense anymore to construct harmony from thirds. Metal uses essentially Pythagorean-based harmony again, in which scales and modes matter a lot, not the major/minor story that some educators today like to derive from stacked thirds (which IMO makes mostly sense in Jazz, but not in many other genres).
Hence, diminished and augmented fifths can't be compared at all with powerchords, at least not when rendered in 12-edo. Though they are most definitely useful as dissonances, and in fact thus employed quite a bit in blues as well as in metal.