Buy a thick cable and a thin cable and compare them. It's the only way you will know if a thicker cable will make a difference for you. 13? I have no clue what you mean.
13 AWG is freaking HUGE. That's got enough carrying capacity that I could use for an extension cord for a radial arm saw....
Most mic cable is around 20 AWG, with 18 being about as large as any mic or instrument cable is likely to get, and 24 being about the smallest you'll probably see. In theory, you might be able to find some 16 AWG shielded cable for specialty purposes, but it isn't common. Definitely not 13.
That's probably speaker cable wire. You can't possibly have a shielded twisted pair at 13 AWG.... It would be as big around as your thumb. Okay, I'm exaggerating a little, but not by all that much....