Most of my time with my hd800 has been Tidal HiFi>Mojo/Hugo>silver dragon>hd800SDR because historically I prefer a portable set up. All along I've had a nice tube amp available but only lately have I started to use it as part of a bedroom setup: Tidal>Hugo>Cayin Ha1a+Expensive Old Mullards>Silver Dragon>hd800SDR.
I never did use my stock cable much and only lately, after owning the hd800 for 5 years, have I become interested in testing the difference between my 2 cables.
All the changes I've been making lately are to max out my hd800 experience. I've learned 2 things:
First, the Moon cable does improve the experience. It's worth the improvement at the used price I payed but I'm not sure I would pay retail because...
...adding the tube amp made a bigger difference. This is the second thing I learned. If I had to start over with building a system around the hd800 I would concentrate on the amp/dac/tubes part first.
The stock cable sounds fine to me. Even though I enjoy what the dragon adds, when I put it away for awhile my ears "forget" and become accustomed to the stock cable.
**Something I read recently about cables: the higher the quality of the gear, the more discernable the difference between cables. I agree.
The difference between stock and silver dragon is greater when Hugo is part of the chain. When I use ONLY the Cayin, the difference is less noticeable.
As for what exactly is different between cables, I couldn't tell you precisely. I decided early on in my headphone journey that I was simply going to enjoy the music rather than analyze. Therefore, all I can say, using songs I know well as a reference, is that I "enjoy"

the songs more with the silver dragon. Again, I'm undecided if the added enjoyment is worth the retail price. 5 years ago I paid $150 used. Retail today is $400. Ouch. I think I would rather hunt some nice tubes, instead.
BTW, I ended up learning all of the above because I wanted a Focal Utopia. After hearing the Utopia, it became a bit of a unicorn for me. Nice to dream about but not very realistic. Instead I turned to maxing out my hd800 setup. I have no regrets. The hd800 is truly endgame worthy for me because it scales up so nicely and in such a noticeable way as I add to or alter the chain.
I'm happy with what I've got and my only question is: do I like the silver dragon because it's a higher quality cable or because I like the silver cable vs the stock copper? Hmmm.....