Awesome question and I think it would be fairly easy to surmise that the American War for Independence was one of the least chaotic and/or violent revolutions/rebellions. As to how to qualify that...well I suppose it depends on quite a few variables. By the numbers: deaths in battle and from all related casualties was relatively low for the Americans. Under 50,000 total deaths (Peckham, 1974).

Some estimates of deaths between British, French, Spanish, Hessian, Native American, etc... are estimated around 100,000. I could cite more sources here, but for the sake of time and self-education a good starting point might be here: http://necrometrics.com/wars18c.htm

To compare only revolutions during the 18th Century and in the Western Hemisphere the American Revolution had a low death toll. Executions alone in France were higher than the KIA numbers of all battles in the American Revolution. Some estimates put the French Revolution deaths higher than 400,000--I caution by saying estimates.

I would feel comfortable saying that the American Revolution was one of the least violent revolutions based on estimated casualty reports.

As to the power vacuum and least radical change in government structure: The new government formed was a radical departure from a monarchy and events that took place during that change led, in part, to the American Civil War. You could argue that the newly founded nation's people would have gladly had Washington as their monarch, but that would have failed as there was no heir apparent--civil war would have likely followed. To that extent a power vacuum was avoided. States rights was perhaps the biggest long-term power vacuum.

I think it is safe to say that the American Revolution was the precedent to follow in future revolutions since it was fairly stable soon after the war ended and the French--among others--tried to mimic the Revolution's success. That is subjective and speculative, but it does fit into the argument for least violent, etc... In other words, the least disruptive, least violent, and most stable government after a revolution is the best road map ergo the American Revolution was the studied road map of future revolutions.

Perhaps unique to the American Revolution is it's success long-term and in which form the cessation began. Before the Declaration of Independence there was many attempts to reconcile differences. In other words, the first thought of the colonies was to stay colonies. To depose the king (in absentia) and his representatives was not the desired outcome. The British Realm was their distant home and greatest trading partner. I think it would be safe to say the American Revolution came about reluctantly. For that reason it is unique and most likely attributable to being less violent and less disruptive than other Revolutions.

Final point, in the larger world view, the American Revolution pales in comparison to Chinese revolutions and rebellions. Death tolls are measured in millions, not thousands.

I hope this helps some...

... very interested to hear other POVs.

Howard H. Peckham, ed., The Toll of Independence: Engagements and Battle Casualties of the American Revolution (Chicago: University of Chicago Press, 1974