Idea Summary
Somewhere along the line APEX changed the aliases for the friendly url to lower case and converted page alias to lower case (can't remember exactly in which upgrade). This is not very consistent, though.
Application Alias in the Application Definition is always automatically converted to upper case.
Page Alias on the page designer is always automatically converted to lower case.
APP_ALIAS and APP_PAGE_ALIAS substitution strings are upper case.
Friendly URLs are all lower case.
The idea is to introduce either new APP_ALIAS_LOWERCASE and APP_PAGE_ALIAS_LOWERCASE substitution strings (for backwards compatibility), or have some application property to always return these strings in lower or upper case.
Use Case
Create all lower case friendly URLs when using, for instance, this target URL
javascript:apex.navigation.redirect ('r/mycompany/&APP_ALIAS./&APP_PAGE_ALIAS.?session=&APP_SESSION.)