Try not to think of it in terms of power chords and barre chords. A power chord is just a chord with a note missing (the 3rd), and a barre chord is just a chord shape.
A recording like the one you linked to probably has about 4-8 guitar tracks on it, if not more, to make it sound the way it does. It's as much about the mix and production as it is about the chords.
But the most useful answer I think is this: when you learn a chord, don't learn it only in one position. For example, find out how many different ways there are to play an E chord, and at what positions on the neck. If you do this for all the chords you use, you'll have a good idea of writing parts to go above your power chords.
Hope that helps