The single most important part of note-taking is that it represents a coherent summary of the important points reviewed in class. Perhaps the worst thing a student can do is attempt a verbatim or semi-verbatim transcription of everything an instructor says. There are studies which have shown that the main benefit to note taking is that in the effort to excerpt important points and put them in your own words you enhance your understanding of the structure of the material, something that does not happen with transcribing. A strong note-taker generally writes less, but in a more focused and coherent way than a weak note-taker.
Another major difference is preparation. If you have done the reading or homework for the class, then your notes can reflect what your instructor says that isn't immediately present in or obvious from the textbook, and understand the material being covered better. Thus good preparation is the key to good notes.
Sometimes you may not be able to write fast enough.
If only one person takes notes, it may not be totally accurate as it's normally that persons interpretation of what's said.
Hope that somewhat helps.
Someone may have more details.