I use dyneema synthetic rope and love it.
Its lighter, so not only are you carting 9kg's less over the front end, but when you are climbing up a hill looking for a spot to winch from its much easier.
It doesnt retain any memory, so when you uncoil it it doesnt want to spool up in big ringlets on the ground.
Its easier to spool it back on the winch.
It doesnt give you wire splinters, or if one strand brakes youre not going to get that sticking in your hand or somewhere.
If it does brake you can just tie a not in it to get you out of the s#!t.
its pretty much maintenance free.
Its safer, when and if it does brake it isnt going to recoil and possibly hurt/damage someone or something.
Wire cable does have a few benefits.
eg...can handle heat, this is important as some winches brake and gearbox's generate allot of heat and can not run synthetic rope.
If you use it allot in sharp rocky terrain it will out last rope, obviously it will handle being dragged over rocks better then rope.
Cable is cheaper to replace.
For me the advantages of rope, well and truly out way the disadvantages.