Wire wrap wire quality
If you're using an automatic cut-strip-wrap bit on the wire-wrap gun, use the Kynar wire. Otherwise it cuts, strips, and wraps, but not necessarily in the correct order! I had trouble with the wrong wire - often there were breaks inside the first (insulated) turn round the pin, so a successful looking joint was actually open circuit.

If you're using the normal (much slower to use) bits, or a hand wire-wrap tool, then either wire is fine.

The wire wrap gun, with the correct bit, correct wire, and practice was probably 20x as fast, maybe more. 

The gun I used was the green Gardner-Denver one, (eBay link) only 240V. Nowadays available from Weller (price has gone up a little). As for the bit ... I couldn't get their own Cut/Strip/Wrap bit to work worth a damn. In the end I had to phone a friend at the BBC and beg him to find the right part : from an obscure British manufacturer probably long gone. However the tool looked a bit like a precision-made version of (and worked like) this description.

I can vouch for the gun. I can't remember any longer whether Kynar or Tefzel wire gave the higher success rate. And I can't vouch for the specific bit shown, though it operates on the right principle (you insert the wire at the tool end, and the cutter 1 inch up trims it to length). But I do remember the right tool, wire, and technique gave a huge productivity increase and very low failure rate.