ASOS is more sophisticated than AWOS and is designed to provide the necessary information to generate actual weather forecasts. It can provide the continuous, minute-by-minute observations necessary for a METARs and TAFs.
ALL ASOS systems can determine type and intensity of precip, thunderstorms, and obstructions to vis as well as peak wind, shifts, gusts, pressure changes, etc.
On the other hand, there are multiple types of AWOS with different capabilities, and they can be purchased by either the FAA or other groups and airport personnel:
AWOS-A: Only altimeter setting
AWOS-1: Altimeter, wind, temp, dew point, density alt.
AWOS-2: AWOS-1 plus visibility
AWOS-3: AWOS-2 plus cloud/ceiling data
AWOS-3 P: Adds a precip TYPE identifying sensor
AWOS-3 T: Adds a thunderstorm/lightning reporter
AWOS-3 P/T: Combines the above two
AWOS-4: Contains all the AWOS-3 systems plus precip occurrence, type, accumulation, freezing rain, thunderstorm, and runway surface condition sensors.
They normally don't go that in-depth on the oral, though
