List processing inside a class

Say I have a class A that has a list of related elements (the type of elements doesn't matter):

public class A {
  private List<String> list;

  public List<String> getList() {
    return list;
  }

  public void addElement(String element) {
    list.add(element);
  }
}

Now I want to access this list from another Client class. I need to add a new item. A more philosophical question is how best to do this from a design point of view.

public class Client {
  private A a = new A();

  public void method1() {
    a.getList().add("");
  }

  public void method2() {
    a.addElement("");
  }    
}

If anyone can point out any advantage of any of these methods, it would be very appreciated. Thank.