Rime is part of my standard bass workout; I play it several times per week. I'm gonna guess you guys haven't picked up a guitar and played it lately, because it is far more complex than either ATG or WTWWB.
The structure is far more convoluted than most (if not all) Maiden songs, and this isn't simply due to length. (If length were the issue, WTWWB would be similar, but it ain't.) Go ahead, count the riffs, write out the structure: there's simply more packed into that song.
Beyond that, the song is full of little details to be nailed. All the places you need that quick little d-e-f#-d run on the fourth beat, vs. all the similar moments you don't play it. The application of dynamics is mandatory; Alex and WW are much more dynamically static. Most time changes are rhythmic modulations, not simply odd time sigs. And if you think that spooky section in the middle is easy, try it on bass: those are some rarely-used bass chords, and playing perfects triplets at extremely slow tempo for several minutes is far harder than you might think.
