Armageddon that comes with Anthology is a stand-alone. Which means that it doesn´t need Doomsday.
Armageddon that is bought from GamersGate is not a stand-alone. That version needs to be installed on top of Doomsday.
Also note that the patch called HoI2DDArmageddonPatch1_2.exe will (with the Anthology stand-alone) try to patch into C:\Program Files\Paradox Interactive\Doomsday.
You must switch this to C:\Program Files\Paradox Interactive\Armageddon.
If you use the "manual browse" that comes with the patch it will try to install into C:\Program Files\Paradox Interactive\Armageddon\Doomsday.
You must manually backspace to get rid of the "Doomsday" part so it reads: C:\Program Files\Paradox Interactive\Armageddon
Only then will it patch properly.
And if you patched it into C:\Program Files\Paradox Interactive\Armageddon\Doomsday, you will get the milestone error if you try to run Doomsday (since you patched Doomsday with an Arma patch). I mention this since I needed to reinstall (after a proper uninstall) and, again, forgot exactly how to do it.
I have now written it into my manual so even "I" will remember months from now.