I'd like to use an object across AppDomains.

For this I can use the [Serializeable] attribute:

[Serializable]
class MyClass
{
    public string GetSomeString() { return "someString" }
}

Or subclass from MarshalByRefObject:

class MyClass: MarshalByRefObject
{
    public string GetSomeString() { return "someString" }
}

In both cases I can use the class like this:

AppDomain appDomain = AppDomain.CreateDomain("AppDomain");
MyClass myObject = (MyClass)appDomain.CreateInstanceAndUnwrap(
                   typeof(MyClass).Assembly.FullName,
                   typeof(MyClass).FullName);
Console.WriteLine(myObject.GetSomeString());

Why do both approaches seem to have the same effect? What is the difference in both approaches? When should I favor the one approach over the other?

EDIT: At the surface I know that there are differences between both mechanisms, but if someone jumped out of a bush and asked me the question I couldn't give him a proper answer. The questions are quite open questions. I hoped that someone can explain it better than I could do.