No difference. They are both able to update everything.
But, since the Stand-Alone Addon Manager it's always updated whenever we update the online files that are downloaded by the Live Update, if you download and install the latest version of the Stand-Alone Addon Manager, it might not be affected by a firewall/antivirus that is blocking the Live Update from downloading, since the files which were going to be downloaded, would be contained in the Addon Manager installer, but ONLY the core program files (executables, the GSX code), and NOT things like additional liveries, updated GSX or scenery objects, AFCADs, textures, sounds.
This means, if your antivirus/firewall is preventing the Live Update from downloading, the Stand-Alone Addon Manager should at least be able to update the core program files, but it will still rely on the Live Update to complete everything else.
