The history of Q is a great companion to Gary's low n slow/hot n fast comparison.
Before the age of manufactured smokers and electronic timers, cavemen most likely discovered the difference in meat cooked directly over a hot fire, and the tender, fall-off-the-bone meat of animals scavenged after a forest fire. After a few grunts, they most likely experimented with ways to mimic the difference. Protect the meat, bury it, build a fire on top of the pit, and forget about it for a day or two most likely morphed into low n slow. I'll bet they indulged in a lot of fermented berries and inappropriate grunts to pass the time until the meat was dug up. Indigenous peoples have been concocting various methods of low n slow indirect heating ever since to make tough, inedible cuts of game tender and juicy. Their methods eventually turned into ovens, smokers, grills, and barbeques.
Having personally done both low n slow, hot n fast, and now a combination of the two, the main advantage of low n slow is the window of time when the meat is finished. That window is smaller with hot n fast, much larger with low n slow. Its all about the physics of heat transfer. The larger the difference in temp between the meat and the smoker/oven/cooker/whatever, the faster the heat transfer to the meat. The smaller the difference, the slower the heat transfer. Anyone who has smoked a butt low n slow, at 210-225F, knows it can take two or three hours or more for a butt to go from an IT of 195 to 205F. Hot n fast, say 300F, it can bridge that time in an hour or less. The meat goes through the exact same breakdown process whether low n slow or hot n fast, but without an electronic thermometer, you have a better chance of catching the perfect doneness when cooking low n slow due to the larger window of time. The key is not to get impatient.
Personally, whether smoking butts or brisket, I smoke low n slow until the stall is finished, then crank my smoker up to hot n fast to finish. Why? Because I haven't mastered being patient. In the process, I maximize smoke exposure, get great bark, and can better control the time the meat is finished to probe tender. Fermented berries, hops, and inappropriate grunts are still great companions while waiting for the meat to exit the heat.