The trailblazer take down buck saw is one that I used to have. It is unique out of those on that page in that it is a full size buck saw when assembled and cuts like one. The chief advantage of this saw, and unlike most back packing saws, is that you can get a firm two handed grip during the cut. This thing will bite through wood as well a bucksaw without compromise in cutting performance. The compromise is the weight. It does pack nicely in its tube and the tube does fit nicely in most packs, but it takes up much room or is heavier than the standard one handed folding saw.
If cutting 6-8" rounds from trees is something you are going to do regularly then this is the backpacking saw you want to have on hand. If you are cutting smaller pieces like 2-3" then most folding 'Sierra-type' saws will work. I haven't experienced them, but from what I've read on these forums, the Silky saw brand are considered the top brand to have. For the little stuff, though, just about any saw will do.
I've used the manual chain saws and they work, but they are kind of gimmicky and don't really let you get into a cutting groove. They are good emergency pieces because they fold flat and tight but are still kind of heavy. I found that a folding saw will outcut the manual chain saws. The wire saws vary in quality by manufacture. They are kind of crap for actually cutting wood but can be used as a piece of emergency kit. The little folding piece of hacksaw isn't meant for cutting wood. Its more meant for SERE kind of things, cutting through fencing on escape ect. or acting as a scraper for firesteels.
My recommendation - if you want to cut big wood, get a good axe and a the take down trail blazer buck saw. You can process a weeks worth of firewood in a day for base camping with that combination. If you are just out backpacking and will make a little fire for cooking or just some nightly entertainment, a folding saw and fixed blade will do you fine.