I should know better than to jump in on a speaker cable discussion, but I guess not...
Roger Sanders got me started building ESLs and his opinions carry some weight with me.
Here's a link to Roger's white paper on speaker cables for ESLs:
http://www.sanderssoundsystems.com/technical-white-papers/54-cables-white-paper
And this is the specific cable Roger used in the custom ESL cables he marketed:
MOGAMI® - W3082 Superflexible Studio Speaker Cables
I used these same Mogami cables on my old perf-metal ESLs, and they sounded great.
Later, I became intrigued with cross-connected coaxial speaker cables. Here's a quote by the cable's designer, Jon Risch:
“Cross-connection is used to reduce the inductance to an absolute minimum. Merely paralleling the center wire and shield would create two separated different polarity composite conductors with an inductance much higher than the cross-connected pair.”
Here's link to my build page with photos for my DIY Jon Risch cables:
Cross-Connected Coax Speaker Cables
These Teflon jacketed coax cables are pricey, each speaker cable uses two of them, and they are very stiff/inflexible, but they do sound wonderful.
After moving my system to a different room I needed longer cables, and I didn't want to spend so much for Teflon jacketed cross-connected cables, so I used much cheaper 12-2 Blue Jeans cable. Guess what: They sound wonderful too.
All of my DIY cables had similar resistance but different ratios of inductance/capacitance, so it follows that there would be measurable differences, especially in the ultrasonic region, resulting from their interaction with the ESL's transformers. However, I wasn't equipped to make those measurements.
I suspect the ultra-low inductance Mogami cables, and the low-inducance Jon Risch cables may have a beneficial effect on impedance (i.e. damping the ultrasonic response peak; thereby mitigating its coincident impedance minimum), compared to conventional 2-wire cables-- but I didn't make any measurements to confirm that. This alone would tip the scales in favor of the Mogami or Jon Risch cables, even though I can't say they sounded any better than the 12-2 Blue Jeans cables.
Perhaps if I had a setup to readily switch between cables for A/B comparisons, I might have been able detect audible differences, but I didn't, and I must say they all sounded wonderful.
I concluded that the cables I've used made no significant difference in my listening pleasure. And I'm guessing most cables of similar gauge would sound as good feeding my wire-stator ESLs.
It was fun building those DIY cables, and the experience convinced me that it's better to spend the big bucks on speakers and electronics and then spend whatever you like on cables.