So if anyone wants one particular definition of "brilliant yet complex pop music" (mine), here's some examples.
Gentle Giant:
Not totally my thing anymore, but is pretty much the definition of "complex, classically oriented prog rock". The counter-argument for every discussion like the one in this thread.
Punch Brothers:
Bluegrass reaching its potential. This band has (unsurprisingly) mad classical influence, but this song? Pure, dissonant pop. Hooks galore.
SiKth:
Warning: death-ish metal with potentially grating vocals. Metal is a fascinating genre simply because of the purely dissonant tonal language it tends towards, and nowhere is that easier to see than siKth. If you get past the potentially annoying vocals and metal timbre of the music (which like, none of you will, I'd guess), the rhythms and tonality is incredibly ambitious and complex. Like, INCREDIBLY complex. Yet still...it's pop music, or at least it uses the form of pop music. Yea, it's metal, but in terms of chorus/verse/bridge sort of structure, it's pop.
Björk:
You all know her. But particularly on the album Vespertine, she pushes hard. I'm not gonna talk about it, because I think this song in particular speaks right to the soul. If you disagree, we don't have much to talk about.
Just my two cents. If you peak harder at pretty much every one of these artists, you'd find that they all love classical music. But times are a-changin', so they don't make classical music.
EDIT: Damn, composer phil dude. We joined the same date, yet you been buuuusy post-wise! Already like 13x my post count...