We have operated an AMS laboratory at the University of Arizona since 1981, as a shared facility between the Departments of Physics and Geosciences.
Standard c14 dates require amounts of between 1 and 10 grams of charcoal; AMS can use as little as 1-2 milligrams, and under special circumstances to samples as small as 50-100 micrograms.
Desmond Clark (1979:7) observed that without radiocarbon dating "we would still be foundering in a sea of imprecisions sometime bred of inspired guesswork but more often of imaginative speculation." And as Colin Renfrew (1973) aptly noted over 30 years ago, the "Radiocarbon Revolution" transformed how archaeologists could interpret the past and track cultural changes through a period in human history where we see among other things the massive migration of peoples settling virtually every major region of the world, the transition from hunting and gathering to more intensive forms of food production, and the rise of city-states.
However, as with any dating technique there are limits to the kinds of things that can be satisfactorily dated, levels of precision and accuracy, age range constraints, and different levels of susceptibility to contamination.
AMS dates are therefore more precise and require smaller samples.
For more detailed information on this and other dating techniques used in archaeology, see the Dating in Archaeology Short Course.