List<MyType> list1;
List<MyType> list2;

Enumerable.SequenceEqual(list1.OrderBy(t => t), list2.OrderBy(t => t))

public static bool ScrambledEquals<T>(IEnumerable<T> list1, IEnumerable<T> list2) {
  var cnt = new Dictionary<T, int>();
  foreach (T s in list1) {
    if (cnt.ContainsKey(s)) {
      cnt[s]++;
    } else {
      cnt.Add(s, 1);
    }
  }
  foreach (T s in list2) {
    if (cnt.ContainsKey(s)) {
      cnt[s]--;
    } else {
      return false;
    }
  }
  return cnt.Values.All(c => c == 0);
}

public static bool ScrambledEquals<T>(IEnumerable<T> list1, IEnumerable<T> list2, IEqualityComparer<T> comparer) {
  var cnt = new Dictionary<T, int>(comparer);
  ...

// lists should have same count of items, and set difference must be empty
var areEquivalent = (list1.Count == list2.Count) && !list1.Except(list2).Any();

// check that [(A-B) Union (B-A)] is empty
var areEquivalent = !list1.Except(list2).Union( list2.Except(list1) ).Any();

var a = new[] {1, 2, 3, 4, 4, 3, 1, 1, 2};
var b = new[] { 4, 3, 2, 3, 1, 1, 1, 4, 2 };

// result below should be true, since the two sets are equivalent...
var areEquivalent = (a.Count() == b.Count()) && !a.Except(b).Any();

var set1 = new HashSet<MyType>(list1);
var set2 = new HashSet<MyType>(list2);
return set1.SetEquals(set2);

list1.All(item => list2.Contains(item)) &&
list2.All(item => list1.Contains(item));

list1.All(item => list2.Contains(item)) &&
list1.Distinct().Count() == list1.Count &&
list1.Count == list2.Count

static bool ArePermutations<T>(IList<T> list1, IList<T> list2)
{
   if(list1.Count != list2.Count)
         return false;

   var l1 = list1.ToLookup(t => t);
   var l2 = list2.ToLookup(t => t);

   return l1.Count == l2.Count
       && l1.All(group => l2.Contains(group.Key) && l2[group.Key].Count() == group.Count());
}

// veriables been used
List<T> diffList = new List<T>();
List<T> gotResultList = new List<T>();



// compare First field within my MyList
gotResultList = MyList1.Where(a => !MyList2.Any(a1 => a1.MyListTField1 == a.MyListTField1)).ToList().Except(gotResultList.Where(a => !MyList2.Any(a1 => a1.MyListTField1 == a.MyListTField1))).ToList();
// Generate result list
diffList.AddRange(gotResultList);

// compare Second field within my MyList
gotResultList = MyList1.Where(a => !MyList2.Any(a1 => a1.MyListTField2 == a.MyListTField2)).ToList().Except(gotResultList.Where(a => !MyList2.Any(a1 => a1.MyListTField2 == a.MyListTField2))).ToList();
// Generate result list
diffList.AddRange(gotResultList);


MessageBox.Show(diffList.Count.ToString);