Old version not transferring
Even if you could copy the application bundle, it wouldn't copy data like emails or calendar events. The data for Mail is stored in ~/Library/Mail/ and ~/Library/Containers/com.apple.mail/. The data for Calendar is stored in ~/Library/Calendars/ and ~/Library/Containers/com.apple.iCal/.

If you didn't already try it, try using Migration Assistant to copy the files from the old installation.