== tests for reference equality.
.equals tests for value equality.
Consequently, if you actually want to test whether two strings have the same value you should use .equals (except in a few situations where you can guarantee that two strings with the same value will be represented by the same object eg: String interning).
== is for testing weather two strings are the same object.
// These two have the same value
new String("test").equals("test") ==> true
// ... but they are not the same object
new String("test") == "test" ==> false
// ... neither are these
new String("test") == new String("test") ==> false
// ... but these are because literals are interned by
// the compiler and thus refer to the same object
"test" == "test" ==> true
It is important to note that == is much cheaper than equals (a single pointer comparision instead of a loop), thus, in situations where it is applicable (ie. you can guarantee that you are only dealing with interned strings) it can present an important performance improvement; however, these situations are rare.