The major advantage is that teflon doesn't melt even at 300 degrees (C), so the insulation won't melt-back from the end of the wire as you work on it. This is really important when working on tiny (SMD) components.
Other advantages of PTFE coated, stranded wire: flexible, good insulation strength, won't crack when cold (even in liquid nitrogen), won't melt when hot (300 degrees), good dielectric properties.
But...PTFE is really really slippery...it's near impossible to grip with fingers while stripping it. Automatic wire-cutters usually break the wire. Here's a way I found of doing it, even for really short pieces.
Step 1: The Wire
(This one is Farnell product code 118-3978. 7 strands of wire, 0.7mm outer diameter).
Step 2: Modify Some Wire-cutters
Step 3: Strip One End (the Easy Bit)
Because it's attached to the reel, the wire is easy to grip. Otherwise, it will just slide through your fingers.
Step 4: Get Something Really Grippy to Hold a Short Piece
First, measure the length of wire needed on the PCB. It may only need 10 mm of insulated length.
Then, grip the insulation using a piece of rubber and some ordinary pliers. Use the modified side-cutters to strip the other end.
The best sort of "rubber" is adhesive-lined heatshrink tube: get some of the 30mm diameter tube, and cut a piece from it. This is really grippy, even on PTFE, and the rubber protects the insulation even when gripping tightly in the pliers. The adhesive is slightly tacky when unused.
Close both pliers and cutters firmly (the cutters won't cut the core, due to the dent we made).
[Do it right the first time, else the cutters will mangle the insulation, and the result will be poor]
Option: if you are prepared to dedicate a pair of pliers permanently to this task, sleeve them with this heatshrink tube: the adhesive-lined high-shrinkage type has a thick wall which gives good, long-lasting results.
Step 5: Tin the End (repair Fractures)
Tin it right back to the end of the insulation: as this photo shows, it won't melt or creep back. This lets solder flow into the end of the wire, and will repair any nicks and fractures that you made when stripping the end.
Then cut the end short: typically 1mm of exposed wire is enough.
Step 6: Use It
In this example, I am soldering a line-driver onto a PCB to extract the clock signal. The chip in the middle is a FIN1001 (SOT-23 package) with 5 legs. Even with a fine iron, and 0.5mm thick solder, this is tricky. Fortunately, the non-creeping property of the insulation allows for a relatively neat job without shorting.
Some bonus tips:
* Tin/Lead solder is better for PCB rework than the lead-free variety: it melts 40 degrees lower (189 vs 227). A temperature controlled iron is essential, as is a really sharp bit. Because the wire is thin, it doesn't conduct heat too fast, and it's possible to hold the end by hand.
* The best way to mount the extra components is to glue them first. Place a drop of superglue on the mounting point (apply with a fine wire, not straight from the bottle). Then glue the SMD component down, on its back.
* If taking the wire off the board, add extra strain-relief. Because it's so slippery, knots will need at least 3 turns.