Global vs user Applications Folder
/Applications is, like you said, global.  Apps run from that folder have no different permissions or privileges if they were in any other folder.  It's the same as running an app in the ~/Downloads folder, it's just neater to have the global /Applications folder.

Having said that, apps in the ~/Applications folder are limited to being run by that user since the ~/Applications folder will have permissions on the folder for the user they're contained in.  

In my hunting around, the ~/Applications folder has global read-only access, but that can vary if a user decides to modify the ACLs (Access Control List) aka permissions.

Hope that clears it up for you!