I usually use 5/16" or 3/8" chains with a grab hook on one end and a slip or choker hook on the other. I also have premade 3/8" cable chokers that feature a slip hook with a socket for the small lug on the end of the cable, which makes it easy to pass under a log. And, I also have 5/16" cable I cut into pieces a few feet long, to wrap around trunks; I put both ends into cable grips.
One main concern with cable is that it is much easier to damage. Dragging a log over rocks or pavement will break lots of wires!
I think lang lay cable would work better for this kind of thing than ordinary lay cable. In ordinary lay, wires are twisted into strands in one direction, and then the strands twisted into cable in the other direction. In lang lay, both twists happen in the same direction. An ordinary lay cable has wires that run along the cable length on the surface, making it easier to slip, but a lang lay cable has wires that run circumferentially on the surface, so it grips.
If you were picking a cable to use to saw through something, lang lay would obviously be the way to go.
But I can't find the stuff for sale!