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.