Personally I recommend screened cable, particularly for low level signals or where the impedance might be on the high side. What's the rationale behind braided interconnects? They tend to have lower capacitance than screened cables but for one or two meters the capacitance probably isn't significant anyway. So what's the advantage of braided cable?
I'm pretty sure that "screened" cable must be the same as what some of us refer to as shielded cable. Most audio interconnects are shielded, with a single center conductor, in my experience. Then there is microphone cable, with two insulated conductors inside a shield. I have some Mogami cables that are also marked, "Neglex 2534 microphone cable." Mogami supplies it as audio interconnect cable with RCA plugs. Shielded cable, microphone cable, and braided Kimber Kable all sound a little different. The latter sounds more detailed and slightly brighter to my ears; and the sound stage sounds more holographic in height and depth.
The rationale? I don't think Kimber, for one, offers a technical explanation.** They do make specific claims about the sound, and the claims become more elaborate with increasing price. The general idea with braided cables is that you don't really need shielded ones unless you are near a strong radio frequency source; so if you can hear something you like with braided cable, and don't really need shielded ones, go for the braid. That, at least, is my rationale.
Here's where I begin to wonder where the rationale is. Take Crystal Cable, for instance. It is very small in diameter, and very expensive. I wonder: what is the point of that? And Audioquest, with their whole stable of cables named after snakes, mountains, rivers. And why name them after snakes? Are they trying to say they are selling snake oil? Hollow air filled insulation tubes between the wires, claiming superior dielectric properties that won't smear the sound by storing and re-releasing energy? Capacitance does that to some extent, no matter what the insulation is made out of.* Can anybody really hear that difference?
Some cable is made from silver, which is a little bit lower in resistance than copper. The slightly lower resistance may not matter, but when the cable surface oxidizes, silver oxide remains a good conductor. Not so for copper oxide, which actually rectifies the signal. This makes a difference at termination points.
No matter which manufacturer it is, I suppose there is at least a little snake oil in all of them, along with some science. I think there is a little less snake oil and a little more science in Kimber's braided cables.
Well, that's enough of my rambling.
*Edit: There is a discussion on YouTube where one of the participants, I believe from MIT Cables, says that he minimizes this effect by using insulation with a dielectric constant of two or less.
**In that same discussion, Ray Kimber says he got into braiding to accomplish noise rejection.