Is there any advantage for either approach?
Example 1:
class A {
B b = new B();
}
Example 2:
class A {
B b;
I take it is almost just a matter of taste, as long as initialization is simple and doesn't need any logic.
The constructor approach is a bit more fragile if you don't use an initializer block, because if you later on add a second constructor and forget to initialize b there, you'll get a null b only when using that last constructor.
See http://java.sun.com/docs/books/tutorial/java/javaOO/initial.html for more details about initialization in Java (and for explanations on initalizer blocks and other not well known initialization features).