Efficient comparison of two lists

ListCompare.java

private static void compare(List<String> list1, List<String> list2) {
    Collections.sort(list1);
    Collections.sort(list2);
    System.out.println(list1.size());
    System.out.println(list2.size());

    List<String> listEx1 = Lists.newArrayList();
    List<String> listEx2 = Lists.newArrayList();
    Iterator<String> it1 = list1.iterator();
    Iterator<String> it2 = list2.iterator();
    String leftObj = null;
    String rightObj = null;
    while(it1.hasNext() || it2.hasNext()) {

        if(leftObj == null && it1.hasNext()) {
            leftObj = it1.next();
        }
        if(rightObj == null && it2.hasNext()) {
            rightObj = it2.next();
        }

        if(leftObj == null) {
            listEx2.add(rightObj);
            rightObj = null;

        } else if (rightObj == null) {
            listEx1.add(leftObj);
            leftObj = null;
            
        } else {
            
            int compared = leftObj.compareTo(rightObj);
            if(compared < 0) {
                listEx1.add(leftObj);
                leftObj = null;
                
            } else if (compared > 0) {
                listEx2.add(rightObj);
                rightObj = null;
                
            } else {
                leftObj = null;
                rightObj = null;
            }
        }
    }
    System.out.println(listEx1);
    System.out.println(listEx2);
}