Cables do sound a bit different, mainly because of issues related to capacitance because the signal from passive pickups is very low; thus cables roll off high frequency content as they get longer. In fact, just for fun, try this - take your favorite cable in as low as a ten foot length, and plug it from your guitar directly into your amp. Play and listen.
Then take two foot version of the same cable and do the same thing. It'll be from a little to a lot brighter (yes, I'm that crazy-picky guy who's actually cut cables down to try this).
So you can definitely pick a cable that helps tailor your sound...but there's more! Cables react to EMI and RFI differently. Some pick it up more easily than others due to shielding, etc. And there are great sounding cables that are so stiff I can hardly use them because I literally trip all over them, etc.
When I got the PRS cable as part of one of those special deals, I really liked the way it sounded; I was mostly using Mogami, but in 25 years of studio work I've also got a collection of a bunch of other cables. I won't say it sounds better - that's a matter of taste - but the PRS cable has less handling noise, and was dead quiet, even compared to the Mogami, which is very good cable, and a studio standard for its ability to reject noise.
The other thing I really like about PRS cable is that it is very, very flexible. It lays flat on the studio floor, doesn't tangle, I don't trip all over the cables when I have to move back and forth to the workstation area, or to adjust a mic, etc, with a guitar strapped on. Great stuff! After I got my first cable, I went and bought more for my pedalboard and pedalboard to amp connection, and replaced everything with it. Great stuff, terminated very well (of course I took one apart to see!) and worth the investment.
Anyway, for me the keys are whether a cable tailors the sound the way I like, whether it makes or reacts to noise like EMI/RFI or handling noise, and whether it's flexible enough to not get in the way.