[c#] Check if two lists are equal

I have a class as follows:

public class Tag {
    public Int32 Id { get; set; }
    public String Name { get; set; }
}

And I have two lists of tag:

List<Tag> tags1;
List<Tag> tags2;

I used LINQ's select to get the Ids of each tags list. And then:

List<Int32> ids1 = new List<Int32> { 1, 2, 3, 4 };
List<Int32> ids2 = new List<Int32> { 1, 2, 3, 4 };
List<Int32> ids3 = new List<Int32> { 2, 1, 3, 4 };
List<Int32> ids4 = new List<Int32> { 1, 2, 3, 5 };
List<Int32> ids5 = new List<Int32> { 1, 1, 3, 4 };

ids1 should be equal to ids2 and ids3 ... Both have the same numbers.

ids1 should not be equal to ids4 and to ids5 ...

I tried the following:

var a = ints1.Equals(ints2);
var b = ints1.Equals(ints3);

But both give me false.

What is the fastest way to check if the lists of tags are equal?

UPDATE

I am looking for POSTS which TAGS are exactly the same as the TAGS in a BOOK.

IRepository repository = new Repository(new Context());

IList<Tags> tags = new List<Tag> { new Tag { Id = 1 }, new Tag { Id = 2 } };

Book book = new Book { Tags = new List<Tag> { new Tag { Id = 1 }, new Tag { Id = 2 } } };

var posts = repository
  .Include<Post>(x => x.Tags)
  .Where(x => new HashSet<Int32>(tags.Select(y => y.Id)).SetEquals(book.Tags.Select(y => y.Id)))
  .ToList();

I am using Entity Framework and I get the error:

An exception of type 'System.NotSupportedException' occurred in mscorlib.dll but was not handled in user code

Additional information: LINQ to Entities does not recognize the method 'Boolean SetEquals(System.Collections.Generic.IEnumerable`1[System.Int32])' method, and this method cannot be translated into a store expression.

How do I solve this?

Enumerable.SequenceEqual(FirstList.OrderBy(fElement => fElement), 
                         SecondList.OrderBy(sElement => sElement))

List<T> equality does not check them element-by-element. You can use LINQ's SequenceEqual method for that:

var a = ints1.SequenceEqual(ints2);

To ignore order, use SetEquals:

var a = new HashSet<int>(ints1).SetEquals(ints2);

This should work, because you are comparing sequences of IDs, which do not contain duplicates. If it does, and you need to take duplicates into account, the way to do it in linear time is to compose a hash-based dictionary of counts, add one for each element of the first sequence, subtract one for each element of the second sequence, and check if the resultant counts are all zeros:

var counts = ints1
    .GroupBy(v => v)
    .ToDictionary(g => g.Key, g => g.Count());
var ok = true;
foreach (var n in ints2) {
    int c;
    if (counts.TryGetValue(n, out c)) {
        counts[n] = c-1;
    } else {
        ok = false;
        break;
    }
}
var res = ok && counts.Values.All(c => c == 0);

Finally, if you are fine with an O(N*LogN) solution, you can sort the two sequences, and compare them for equality using SequenceEqual.