I am not a seasoned reviewer by any means, but about Empyrean and HEKse I have both (returning one of the two) running from a W4S DAC1v2 -> V281 (balanced) and WA6-SE (unbalanced) in parallel. I do not have a balanced cable for the HEKse and I find it I like the sound better from the WA6-SE at least single ended. The Empyrean I am running it with a dragon silver cable from an LCD3 I have, connected to the V281 (balanced). 100+ hours on each cans.
Roughly speaking, the sound signature is the same debate as LCD3 vs HD800, only Empyrean and HEKse do everything much better imo. I don't feel like typing much
so I would summarize the difference between the two are in tonality, bass and soundstage.
The leather pads on the Empyrean make the sound really dark and bassy to my taste, they remind me of the Sony's with these pads. The alcantara pad are more neutral and to my liking, they give Empyrean more air and space. Detail retrieval and extension is about the same in both cans.
(From now on all impressions of the Empyrean are with the alcantara pads)
Overall the sound out of the Empyrean feels very balanced, a bit warm and dark but not much, this makes it possible for me to listen to them for very long hours with no fatigue whatsoever. The bass is always present even at low volumes but it never gets over powering, they are also very transparent and natural sounding. If you were to listen to a life performance, the bass rendition of the Empyrean would be much closer to it than the HEKse. This is easily noticeable with jazz, where the background bass notes would almost be lost with HEKse, the Empyrean would give it an slight boost, enough to make it relevant but not distracting. Empyrean performs spectacularly cross the whole range. Where they do suffer is in the soundstage.
Soundstage is a whole lot smaller on Empyrean than on the HEKse. To put it in perspective, Empyrean soundstage is about the size of the LCD4 while HEKse is about the same of the HD800. Both are better in terms on placement and precision compared to LCD and HD, with HEKse having a lot more air, space and separation between instrument than the Empyrean. If bass is a bit better on the Empyrean, I would say soundstage/imaging is whole lot better on the HEKse. There is also instances where the soundstage/imaging on the Empyrean "breaks down" with complex passages, example of this Metamorphosis by World Saxophone Quartet makes for a very unconformable listening experience on the Empyrean, where I find my left and right ears listening to two different rooms, very disconnected. On the other hand the HEKse never losses coherence and accuracy.
I haven't mentioned HEKse much because aside for the bass, everything else is close to perfection if not perfection itself, and you already have a pair. HEKse are very natural sounding with an outstanding soundstage, both in size and presicion. Mids and highs feels so real that sometimes gets spooky with voices and sudden notes.
Summarizing, if you were to ask me, I would say Empyrean bass is half step ahead of HEKse while HEKse soundstage/imaging is a whole step ahead of Empyrean. Tonal differences are a matter of personal taste and everything else is about the same on both.
Hope it helps, If you want to know something specific, ask and I'll do my best answering.
EDIT:
The Empyrian is "dark or warm leaning" sound, but it is a really pleasing sound with a ton of details and very good soundstage. This makes for a very relaxing/comfortable experience, I can listen much longer to Empyrian than to the HEKse for example.
