The main advantage of possessive quantifiers is speed. Since possessive quantifiers never give up what they have matched, no time is spent trying out alternatives. A regular expression that uses them will quickly succeed or quickly fail.
However, unless you are writting an application that does a great deal of pattern matching and that demands speed, possessive quantifiers are rarely useful.
(Review: ) what is the default behavior of a quantifier? greedy, lazy, or possessive?