Okay well I did a bunch of testing with the Atticus (Eikon is coming next week) and one thing is really obvious: these are very different headphones. The Atticus is super mid-bassy and the AEON is super balanced. Your personal preference for tonality will make more a difference than anything else. I happen not to prefer warm headphones and find that the AEON is in a sweet spot for my tonal preferences. That doesn't mean I can't enjoy the Atticus (I definitely do on certain songs), but I'd take the AEON over it simply because it fits my preferences way more often.
With that out of the way, I'll say that the Atticus shined in a few areas: poorly recorded songs and thick, chunky songs. It's more forgiving thanks to its warmer nature. The AEON is revealing, which can be bad on some tracks. Out of the tracks I tested, this was most noticeable on "Under a Glass Moon" by Dream Theater. There's something funky going on with the snare and hi-hat that was prominent on the AEON but nicely smoothed out on the Atticus.
The Atticus also excelled on chunky songs like "Wreath" by Opeth. The bass and drums lay down a thick foundation that really drive the song and the cookie monster vocals have a great presence lower in the freq range that isn't overpowered by the other instruments. It also brings out some of the nice bass work. AEON feels a bit thin comparatively with the machine gun bass drums not laying enough of a foundation, leaving most of the work to the guitars. When the additional guitars come in, they overpower the vocals a bit. This is a track that wants the weight and thickness of the Atticus.
The AEON shined in its own areas: well-recorded tracks and mid-focused tracks. Porcupine Tree has some of the best mastering around and loves the AEON. "The Sound of Muzak" is pure drum porn with the complex rhythms, ghost notes and subtle flourishes. The AEON reproduces the cymbals beautifully, places them perfectly in space and lets you hear everything Gavin is doing. At the same time, the vocals and guitars are clean and detailed and the bass drum is nice and punchy. On the Atticus, you get a more visceral feel to the drums but the focus is more on the driving beat than the subtle flourishes. As a drummer myself (in case you couldn't guess at this point), I find the loss of that detail in the drums to be unforgivable. It doesn't help that the powerful bass bleeds into the mids as times, making the song feel a little busy and confusing instead of clean and intricate.
This leads to my second point about the AEON sounding better on mid-focused tracks. Both do mids well but the Atticus can sometimes get too busy and start to muddy things up a bit. The AEON does mids really well at all times period. "To Rid the Disease" by Opeth has a lot of focus on vocals, piano and strings. The Atticus pushes them back a bit in favor of drums and bass, which doesn't super work for me. The AEON balances everything much better.
Overall though, I think it'll mostly come down to tonal preference as I said before. "Blood and Thunder" by Mastodon has recessed mids right in the recording so you're boned either way. At that point, it's a choice between a focus on the midbass (drums and bass) vs balanced presentation with more prominent mids and highs at the relative expense of some mid bass. "Lost" and "Where the River Flows" by Riverside have the same sort of split. They sound good on both, a little more clarity and detail on the AEON, a little more body and presence on the Atticus. "Dim Ignition" and "Famine Wolf" by Between the Buried and Me is more of the same: AEON feels like it has great mids and highs at the expense of bass presence. Atticus feels really bassy and rumbly at the expense of some clarity in the mids and presence in the highs.
So yeah, a bit of an apples and oranges thing. Most folks should know pretty quickly which they'd prefer based on their personal preferences. For me, the AEON is a no-brainer even though I do like the Atticus better on some tracks. And just to be absolutely clear: the Aeon doesn't lack bass presence and the Atticus doesn't have recessed mids and highs. It's just how they sound relative to each other.
PS - While writing this whole rambling post up, I have been listening to "Eye of the Soundscape" by Riverside. Never heard these guys before, but totally digging this album!