The Ethernet standard has a much more robust error detection and correction algorithms built into it than those protocols specifically designed for audio like S/PDIF, and for very good reason.
if a few bits in an audio stream get mangled, it's not that big of a deal and to the 99% of the people in the world who are not hard core audiophile, most likely not even audible. But if a few bits in a bank transfer get mangled that could be a huge deal, effecting millions of dollars. Ethernet systems work very hard at producing bit perfect communications in spite of the quality of the media doing the transmission. So given that I am not sure there is much to be gained from the use of "premium" cable on the network side of your system. If you are in an area with lots of RFI, Charles' suggestion of shielded cable might be helpful, but other than that, I don't logically see any benefit from premium Ethernet cable, on the internet side of your device.
Now of course will all of that said, there are plenty of things in this hobby that do not follow "obvious logic" so while I don't expect there to be any big differences, I would not be surprised if there were.
With that in mind has anyone in the group tried an audiophile grade Ethernet cable to bring the network or internet signal into a streaming device like for example as a patch cord between a router or network switch and your streamer? and if so, what were the results?