I don't agree with that on the grounds of its lack of consistency, but the best parts of ITPOE are definitely as good as Octavarium. I could see someone thinking it's a bit better overall, but significantly? Nah.
I can't speak for the others but I DO mean significantly. To me the entire intro to Octavarium is a throw away and Someone Like Him is completely out of place. The song never really gets going until Medicate. That's a significant chunk of background noise that I don't find with ITPOE. I've never found ITPOE inconsistent when listened to as one piece.
I disagree. The intro is cool atmospheric buildup that establishes the theme, and Someone Like Him is beautiful with its unique chord progressions. The only part that is weaker for me is Full Circle, just because of the silly lyrics, but musically I still think it's a good section.
Now, I do think ITPOE is still great as a whole too, but Slaughter of the Damned is empty chug with basically one note being sung over the top (is that the right name of that section?), and the instrumental section is forgettable noodling as fast as possible. The rest of the song is great, but for me it just has that huge dip in the middle that holds it back from being something I can listen to easily the whole way through like I can with Octavarium.
See, what you described with ITPOE, that's Octavarium to me. The beginning is beautiful, and SLH and Medicate are great - superb atmosphere, some gorgeous vocal melodies - and then Full Circle comes in it's like... seriously? The lyrics are pretty nonsensical and the music isn't really that good as well. The key solo is pretty boring, I'll never get why some people love it that much. Intervals is great again, the wankery manages to feel tight and works well in the song, and the climax is awesome, with the gradual increase in intensity. That would have been a high note to end it...
...but DT had to segue into one of their most boring and overrated parts. Seriously, that solo is sooooooo god-damn boring. And that doesn't have anything to do with it not being shreddy or anything, because I like slower, more paced solos a lot as well (LITS solo is probably my favourite Petrucci solo), but Octavarium's outro solo is just too long and too little variety. Nothing special, and a completely underwhelming finish.
So while I enjoy ITPOE all the way throughout, Octavarium can be a nice listen once in a while, but ultimately, a few parts hold it back from being great, or even very good.