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StringBuffer: methods are synchronized, available since 1.0.
StringBuilder: methods are not synchronized, available since 1.5.

So, use StringBuffer for compatibility with old versions of Java or if implicit synchronization is desired (bad style IMHO) and StringBuilder otherwise.

(This is really quite a bad interview question.)

StringBuffer is thread safe class. So if in your code, you are using more than one thread, use StringBuffer as it is synchronized. Whereas StringBuilder is not thread safe.
StringBuffer is slower than StringBuilder because of synchronization overhead.

String is an immutable class while StringBuilder & StringBuffer are mutable classes. StringBuffer is synchronized while StringBuilder is not.

Below link can be useful to find more differences between String, StringBuffer & StringBuilder

<a href="newtechnobuzzz.blogspot.com/2014/07/difference-between-string-stringbuffer.html">Difference between String, StringBuffer and StringBuilder</a>

newtechnobuzzz.blogspot.com/2014/07/difference-between-string-stringbuffer.html