I think Octavarium is easily better. So much more cohesive, with more payoff with the variations of the main themes of the song, and it's the first DT orchestral epic, with the ultimate epic outro.
IT's outro falls completely flat to me, and feels too cliche, even using elements directly out of Octavarium and SDOIT.
Octavarium feels "so much more cohesive" because the message of the song is about a full circle. Illumination Theory is about transitioning from a moment of questioning and confusion to a moment of enlightenment, of illumination. That is why there are sharp breaks in between the parts but still manages to harken back to previous themes.
Octavarium, while great, actually has a problematic outro. It sounds great, it sounds uplifting, but I always wonder what exactly happened in the course of the song which would lead to an uplifting ending? is it supposed to be a realization that one has just to accept that one just comes full circle and one is trapped in an Octavarium?
The beauty of Octavarium's outro is that it's
not overly uplifting, or depressing. The guitar solo starts in a pretty dark minor sound, then uses a lot of eery chromatics, to put it off sounding either major or minor in tonality, and weaves between sounding dark and light seamlessly, with some parts being dark, and some parts being very bright.
Here's the best bit - analyze Octavarium's main theme reprise that closes off the song. Each bar actually alternates major and minor key tonality. The first bar has the descending run with the major third, then the next bar is the same run but with the minor third instead, then back to the major key variation, then it finishes with the ascending run in minor.
It fits perfectly with the circular theme of the song, with the cycle repeating, having both positive and negative connotations, but really being neither inherently, because it's such a general theme.
Then it repeats the intro drone of the album to reinforce the cycle repeating (and it actually repeats several cycles in the process, but that's for a deeper analysis), and it's only the root note, devoid of tonality.
The more I analyze Octavarium, the more I appreciate it. It's a song that holds up and only gets better with age imo.