Assuming that braided wire means stranded flexible wire, rather than the unlamented Litz wire that was always a total pig to terminate or the stuff found as the outer shield on co-ax and similar.
Flexible wire, by its nature, flexes. It absorbs vibration and allows you to work around it easily. Rigid bits, like soldered terminations benefit from added stress relief such as heat shrink sleeve over the area where it transitions from solid (solder) to flexible.
Solid single core does an admirable job of putting the electric where it s needed, but does not like vibration. It either provides a weak spot that eventually breaks or transmits the force into whatever it is terminates to, which might, in turn, provide the weak spot.
Working in the vicinity of wire, flexible lets you move the wire out of the way, solid doesn't, or at least, not easily.