Tried both in Munich, would take the Focals over the HD800 any day. Mostly because I’m not a fan of that much treble, but also because the HD800’s imaging seems a bit “stretched” to fit the wide soundstage, and because the dynamics on the Focals really are something!
Headphone cables do not affect sound if they aren’t damaged or defective. There are very few exceptions to that, but that only applies if you have a headphone with exceptionally low impedance, as in single digit Ohms. That neither occurs with any of the common driver types, nor with most uncommon types.
However, they can have a significant impact on the user experience. A cable that’s too short is annoying if not downright unusable, a cable that’s too long is just flopping about everywhere, a cable that’s too stiff is unpleasant and can create microphonics, and a cable with a bad surface can feel and look unpleasant. Add all these factors together and cables do matter, just not for the sound itself.
And thus, I can wholeheartedly recommend Hart Audio Cables. They feel nice, they look good, they have very little microphonics, and their modular system allows you to use different outputs for your headphones with the same cable.
But if a different sound is all you’re looking for, new cables are not the way to go.
I have some personal experience with the T60RP Argon (a mod that is a bit harder to drive) and motherboard outputs.
In my case, the motherboard’s integrated amp was able to provide plenty of voltage, but not enough current, and also not very quickly. So, bass (which needs a lot of power) was weak and less punchy. Even my phone (which has an ESS Sabre DAC comparable to the LG V60) did better here, but in later comparisons I noticed it has a bit of a bass roll-off, too.
I am now using a Qudelix 5k for all my desktop and mobile audio needs, which, even without EQ, provides a notably better bass response than either of those two because the implementation is just better.
I’m guessing you’d have a similar experience. Because it’s a fundamental issue with how much power can be provided, you also can’t fix this with EQ alone, because that doesn’t change what the hardware can do. But you don’t need a very high-end or powerful amp, something small and simple will do, as long as it’s designed properly (like the aforementioned 5k).
There is always the option to wear a pair of noise cancelling headphones over some earbuds/IEMs, which can also be noise cancelling. Alternatively, passive ear protection instead of headphones over your earbuds/IEMs.
Either way, you get two layers of noise isolation.