I have used both the "survival" wire saw, just to experiement, and the one Pocket Chainsaw
http://www.pocketchainsaw.com/ and the latter is far superior, but tbh both are pretty crummy. Sure the Pocket Chainsaw is compact, but its pretty energy intensive if you have to use it for cutting fire wood. I think its the kind of thing you might stash in your car or truck for helping to clear downed tree limbs from the road. Really compact but capable for a short burst of intense work.
If I was going on a trip and expected to need to cut a lot of wood, I would pack a bow saw blade and make a frame for it. The blade is light, but a little hard to pack, but it cuts way better than any flexible saw.
For most things though, one of the folding pruning saws works better than the flexible saws. It is easier to use one to cut small loose wood up for the fire than it is to hold something down for use with the flexi saws.