Google would surely have a more complete answer, but I'd say the main difference is that "place" is a subset of "put"; in other words, you could use "put" in just about any context, but "place" implies a very careful, specific placement of something, and is often used in formal instructions. Examples: Put your coat anywhere. Put the eggs in the basket. Put your head on my shoulder. Place the coat neatly on the hanger. Place the eggs gently in the basket. X-Place your head on my shoulder. (Incorrect)

I agree with Gabbklein - "place" suggests a degree of carefulness.