HE1000se has a major focus on speed and resolution throughout the entire frequency range. It becomes easy to pick apart the mix, and the experience is either like you're listening to a recording or you're in a grand concert hall. The details you hear and can pick apart in any genre is extremely impressive. The tonality leans bright. Bass is tight and extends well, I just wish it had more quantity. I often use a bass shelf around 120hz when i want a little more punch. Both headphones are very light and comfortable, but the Hekse has the edge because of the giant oblong earpads that fully surround your ears.
Atrium focuses more on enjoying the music as a whole. Soundstage is wider, but imaging isn't as precise. There's more than enough detail, and I can still get the lost in the music, only picking out the little details when I want to. Speed and decay are noticeably slower but it allows for a more rich and natural experience. This leans noticeably warmer in tonality. Some recordings on the Hekse can sound unnatural, but sound detailed and rich on the Atrium. Bass is punchy and textured and has more presence on the Atrium, but extends lower on the HEkse. Midrange is always the hardest to describe. I rarely ever try to attempt it, but they just sound so natural here. Treble extends well and offers plenty of detail but isn't as present as it is on the Hekse.
Quick summary: Atrium is slightly warm, euphoric, smooth, forgiving, yet detailed, rich, and punchy. Hekse is exacting and tight, and has more treble focus in comparison. Hekse will show the flaws in recordings for better or for worse, but I prefer the Atrium when I'm not looking for a reference/analytical experience. The Atrium is extremely impressive. Fun factor of Aeolus, mids of the Auteur, most of the detail of the Vérité, widest soundstage of any ZMF, very fun headphone to listen to. This may not be as detailed as you'd need, it was honestly kinda rushed, so let me know if I can answer any more questions to help narrows down differences.