EqualityComparer<T> defauls to the object.Equals method, so the 1) and 2) cases are equivalent to 5) and 6).

I don't see why these comparison should be consistent by default. The true cases happen because System.Type equality implementation is based on the UnderlyingSystemType property. So, you could override Equals(object) and Equals(Type) - BTW, virtual only on Framework 4 -, but that wouldn't fix case 3).

So, what you can do to make sure it is consistent is this:

 class MyType : TypeDelegator
    {
       public MyType(Type parent)
          : base(parent)
       {
       }

        public override Type UnderlyingSystemType
        {
            get
            {
                return this;
            }
        }
    }

With this implementation, all cases will report false, which is consistent, but I'm unsure about the side effects... I suppose it depends on what your code does eventually.