Given the discussions flowing in comments I will try to do this one in plain English:
The main difference between Attached Dependency Properties and Dependency Properties (and therefore between .Register and .RegisterAttached) is that RegisterAttached allows the value to be assigned to any dependency object whereas Register only allows it to be attached to the class passed as the ownerType parameter.
As Haris Hasan mentions (deep in the comment thread), your example is using the only type allowed (i.e. CustomControl) and does not show you that the Attached version can be assigned to ANY dependency object.
e.g. you can do this with your Attached Dependency Property (but not a plain DP):
<Grid local:AttacherClass.ADP1="1" x:Name="LayoutRoot" Background="White">
</Grid>
The best reference for ADPs I can find is this one: http://msdn.microsoft.com/en-us/library/ms749011.aspx
We used ADPs as the basis of a localisation system, so that translations could be parasited onto objects during load rather than using horrendously long bindings. Couldn't do that with DPs
Update:
I would also like to clarify that the parent limitation applies to XAML based use of the attribute. From code the parent limitation apparently does not apply.
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