All the rope winches that I have seen specify using 3 strand.
There is an additional benefit to using three stranded rope: it generally has considerably more stretch then braided rope of the same material. This stretch is particularly useful when using a very slow hand winch, as you can tension the rope considerably prior to making your cut. Once the tree begins to go in the direction of the cut, the additional stretch helps to continue the pull in the desired direction.
I have been known to put a bull rope on a tree attached to our wrecker winch and park as far away as possible. Then I stretch the line until it is really really tight. Make the back cut, and a heavy head leaner will continue to be pulled until it is well over center.