In the price you are looking, I assume you are talking about the older 50-500 EX, and not the new 50-500 OS. I hand hold my Sigma 150-500 OS all the time, but wouldn't like to do so without OS. I'm 34 years old and have 16" upper arms, and the weight of the 150-500 does get fatiguing after a short while of carrying. If you plan on carrying it with a neck strap and only bringing it up to eye level when you need it, then it's not too bad. I know that there are people shooting with the 50-500 EX hand held with good results, but don't know what techniques they use for extended field use. I imagine the majority use environmental support (trees, fences, car roofs, etc...) when they can. OS (IS) takes away the need for that support, at least in short spurts. But the Bigma is still a 4 lb lens. I bet you could get used to a monopod/393 for regular walk-around use without much effort. The 393 is an incredible piece of equipment, by the way.
AS far as AF speed, both the 80-400 and 200-500 are not fast, each using older versions of AF technology. Additionally, both lenses lack a focus limiter switch...an undeniably important factor for distant subjects. My 150-500 has the newer HSM AF motor, which is actually relatively comparable to Canon's USM. But even in this newer lens, lack of a focus limit switch really slows down the hunting time when you miss the AF lock in the first pass. The Canon 300 has a limiter.