My solution is for the cases where you don't care about the ordering within the Lists - in other words: Lists with the same elements but DIFFERENT ordering will be considered to have the same contents.
Example: ["word1", "word2"] and ["word2", "word1"] is considered to have the same content.
I've addressed ordering, I also just need to say something about duplicates.  Lists need to have the same number of elements to be considered equal.
Example: ["word1"] and ["word1", "word1"] is considered to NOT have the same content.
My solution:
public class ListUtil {
    public static <T> boolean hasSameContents(List<T> firstList, List<T> secondList) {      
        if (firstList == secondList) { // same object
            return true;
        }
        if (firstList != null && secondList != null) {
            if (firstList.isEmpty() && secondList.isEmpty()) {
                return true;
            }
            if (firstList.size() != secondList.size()) {
                return false;
            }
            List<T> tmpSecondList = new ArrayList<>(secondList);
            Object currFirstObject = null;
            for (int i=1 ; i<=firstList.size() ; i++) {
                currFirstObject = firstList.get(i-1);
                boolean removed = tmpSecondList.remove(currFirstObject);
                if (!removed) {
                    return false;
                }
                if (i != firstList.size()) { // Not the last element
                    if (tmpSecondList.isEmpty()) {
                        return false;
                    }
                }
            }
            if (tmpSecondList.isEmpty()) {
                return true;
            }
        }
        return false;
    }
}
I've tested it with Strings as follows:
@Test
public void testHasSameContents() throws Exception {
    // comparing with same list => no duplicate elements
    Assert.isTrue(ListUtil.hasSameContents(List.of("one", "two", "three"), List.of("one", "two", "three")));
    // comparing with same list => duplicate elements
    Assert.isTrue(ListUtil.hasSameContents(List.of("one", "two", "three", "one"), List.of("one", "two", "three", "one")));
    // compare with disordered list => no duplicate elements
    Assert.isTrue(ListUtil.hasSameContents(List.of("one", "two", "three"), List.of("three", "two", "one")));
    // compare with disordered list => duplicate elements
    Assert.isTrue(ListUtil.hasSameContents(List.of("one", "two", "three", "one"), List.of("three", "two", "one", "one")));
    // comparing with different list => same size, no duplicate elements
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "three"), List.of("four", "five", "six")));
    // comparing with different list => same size, duplicate elements
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "two"), List.of("one", "two", "three")));
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "three"), List.of("one", "two", "two")));
    // comparing with different list => different size, no duplicate elements
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "three", "four"), List.of("one", "two", "three")));
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "three"), List.of("one", "two", "three", "four")));
    // comparing with different list => different sizes, duplicate elements
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "three", "one"), List.of("one", "two", "three")));
    Assert.isFalse(ListUtil.hasSameContents(List.of("one", "two", "three"), List.of("one", "two", "three", "one")));
}