I'll let the more experienced folks expand on the differences, but for me (for now at least, as my impressions keep evolving as I pad and tube swap with the Atrium) it's a bit as if the Auteur was suddenly on the same level as the Verites. Keep in mind nearly all my time with the Atrium has been with suede versions of pads (as is true with all my ZMFs) which tend to be brighter than their lambskin counterparts.
The overall sound has similarities to the Auteur, with technicalities being closer to the Verites, being more detailed than the Auteur with its own unique and expansive soundstage making it distinct from the Verites and the Auteur. Perhaps it's because it's so open and/or the new dampening, but even more than the Verites I am regularly fooled into thinking a sound is external and having to make sure it's really coming from the headphones and I didn't somehow set my computer to play through my DAC and simultaneously directly through desktop PC speakers. Occasionally there are behind the head sounds which are almost spooky, and again I've had to make sure a sound wasn't actually coming from behind me and not the headphones.
While my first impression, without any burn in or direct comparison, was that it was much like the Autuer, now having spent a couple weeks with it, comparing with the Auteur yesterday the differences seemed greater and that the Atrium was clearly on another level without making me enjoy the Auteur any less. One obvious difference vs. the Verites is getting TOTL sound that doesn't make your crap recordings sound like crap. Songs I'll just skip on the Verites because they're so revealing, sound great on the Atrium. For all those songs I know will never be remastered and sound better, this is probably as good as they're ever going to sound. There is also a punchiness to the bass (which does vary based on pads, for me the BE-2 suedes being the most so of the suedes) which is more than I've experienced with the Verites, and a quality to it which I find very gratifying.
