My personal exsperience is that for most materails a factory serrated, either spyderedge or bechmade, edge will cut through faster than a factory plain edged. I have cut natural fiber, nylon and kevlar strap and line with both and have found the serrated edge to perform better and more consistantly.
My first experience that convinced me of this was with a 4 inch kevlar strap that had been used as a tow line to pull a heavy truck from the mud. The guys had knotted it around the bumper of a mobile drill rig and it was well and truely locked in place after hauling the thing up slope at a hazardous/radioactive waste site. The field manager and I watched these guys hacking and sawing at the strap with a variety of pocket knives (and these boys kept their Case and Buck folders sharp as razors) to no avail. Knowing that I carried more than one knife at any time he looks at me and the following exchange takes place, "They need a knife." "They got knives." "They need a SHARP knife." "Sigh". I squitch-thump downhill, did I forget that it had been and was raining at the time and that I was on a cane from having my ACL replaced, and after a brief and somewhat vulgar explanation from the driller he yanks the strap taught and gives me the "Ok techie puke, let's see what ya got" look. I pulled the Spyderco serrated Delica from my pocket, opened it one handed and cut the strap with one stroke. His, and his crew's, plain edges had been skipping off the strap fibers, but the serrated edge popped them like they were nothing. After that I almost had to buy another knife for them because they kept borrowing mine. I've repeated this with large and small lines and webbing of different materials over and over again.
I have not needed to "saw" with serrated edges, but I have had to take more than one pass at times for very thick materials. Sawing isn't needed and the back and forth motion subjects the user to the risk of cutting themselves. (For those of you that think that only an incompetent would cut themselves this way just remember the serrations are not teeth on a saw and anytime you push towards a blade you risk your warm tender pink parts being rudely introduced to the blade's cold hard silvery parts.)
If you carry a kife for defensive purposes you should never use this knife for other things. It should be left as sharp as you can possibly get it so that should it be needed to save your life it works a well as possible. Carry a second utility knife for the strap cutting, apple peeling, fingernail cleaning and leave the weapon of choice ready for it's purpose. This also gives you an excuse to have more knives, which is always a good thing in my mind!