You are just comparing strings.
Put the values in ArrayList A as keys in HashTable A.
Put the values in ArrayList B as keys in HashTable B.
Then, for each key in HashTable A, remove it from HashTable B if it exists.
What you are left with in HashTable B are the strings (keys) that were not values in ArrayList A.
C# (3.0) example added in response to request for code:
List<string> listA = new List<string>{"2009-05-18","2009-05-19","2009-05-21'"};
List<string> listB = new List<string>{"2009-05-18","2009-05-18","2009-05-19","2009-05-19","2009-05-20","2009-05-21","2009-05-21","2009-05-22"};
HashSet<string> hashA = new HashSet<string>();
HashSet<string> hashB = new HashSet<string>();
foreach (string dateStrA in listA) hashA.Add(dateStrA);
foreach (string dateStrB in listB) hashB.Add(dateStrB);
foreach (string dateStrA in hashA)
{
if (hashB.Contains(dateStrA)) hashB.Remove(dateStrA);
}
List<string> result = hashB.ToList<string>();