If I put terminal ends on a cable (I'm an A/V installer by trade), I put a little solder on the connector (where the terminal end goes) and when I mate the 2, I heat the solder and push the terminal end on so that they stay connected until I reheat the solder to remove them. They sometimes pop off in a touring rig situation if they aren't soldered.
The quick answer is on subs, I use 12ga and on mids and high end drivers, I use 14. Both are braided wire. I have seen solid core (thhn) wire in P.A. installs from time to time but I usually replace it and chuckle to myself.
There has been discussion about how the electrons move over solid core vs. braided. From what I hear, high end stuff moves better over braided wire. It's something about there is more surface area on the conductor itself (being a bunch of small wires "braided" together) and that low end stuff moves better over solid core. I think that the physics of that might be true, but we as listeners would have a time hearing it.
Also, if it's larger wire than is inside the cabs, I might replace that too. I mean, if you buy an AWESOME speaker cable but after your speaker's input jack the cable is crappy, you've just wasted your $ on the "awesome" cable. Speaker cable is all about thru-put.
BTW: 13 ga wire is what is used in Vertec (JBL) P.A. systems these days... for the low end drivers (not the subs).