Difference between constituency parser and dependency parser

A constituency parse tree breaks a text into sub-phrases. Non-terminals in the tree are types of phrases, the terminals are the words in the sentence, and the edges are unlabeled. For a simple sentence "John sees Bill", a constituency parse would be:

                  Sentence
                     |
       +-------------+------------+
       |                          |
  Noun Phrase                Verb Phrase
       |                          |
     John                 +-------+--------+
                          |                |
                        Verb          Noun Phrase
                          |                |
                        sees              Bill

A dependency parse connects words according to their relationships. Each vertex in the tree represents a word, child nodes are words that are dependent on the parent, and edges are labeled by the relationship. A dependency parse of "John sees Bill", would be:

              sees
                |
        +--------------+
subject |              | object
        |              |
      John            Bill

You should use the parser type that gets you closest to your goal. If you are interested in sub-phrases within the sentence, you probably want the constituency parse. If you are interested in the dependency relationships between words, then you probably want the dependency parse.

The Stanford parser can give you either (online demo). In fact, the way it really works is to always parse the sentence with the constituency parser, and then, if needed, it performs a deterministic (rule-based) transformation on the constituency parse tree to convert it into a dependency tree.

More can be found here:

http://en.wikipedia.org/wiki/Phrase_structure_grammar

http://en.wikipedia.org/wiki/Dependency_grammar