They're very different, I have both and prefer each of them depending on my mood. The other reply is correct about the treble on the HD800, I applied the SDR mod and use a tube amp and it is no longer an issue for me.
The Elex is more energetic and has better slam, especially in the bass. The HD800 is very detailed and open. I usually prefer the HD800 for classical and jazz, while preferring the Elex for metal, pop, and rock.
With the Schiit Loki, I think the HD800 is good on every genre. Sometimes I still want the more energetic Elex though. Sometimes I don't. ;)
Please keep in mind everyone's ears/taste is different, you may hate what I like and vice versa.