I'm running Xcode (downloaded from the Mac App Store) on my MacBook Pro running OS X Mavericks.
The weird thing is I am running version 3.2.6, yet Xcode claims to be up to date. There are no updates in the Mac App Store.
You may have Xcode 3.2.6 from an earlier installation and are running it. Note that Xcode 3.x being a pre-MAS (Mac App Store) version, installs into the
/Developer folder (by default, although it can be installed elsewhere too), whereas the Mac App Store versions (from Xcode 4 onwards) install into the
/Applications folder. To run Xcode 5, make sure you're running the application from
/Applications. You can also use Spotlight to find where Xcode 3.2.6 resides on your system.
If you wish to uninstall the older version (Xcode 3.2.6), open
Terminal.app and uninstall it using the command:
sudo /Developer/Library/uninstall-devtools --mode=all
Xcode 4 was a separate download in the Mac App store. Xcode 5 replaced 4 in the app store. That is why you do not see an update. Download Xcode 5 directly from the Mac Appstore. If you would like to keep xcode 3.2 also installed, right click an xproj file and select to open all these files with xcode 5 to make it the default xcode in your system. But there is no reason nowadays to keep such an old xcode installation.
One very good reason in my book would be the interface - not an MDI-like monolithic structure copied from MSVC, but one with a nice, small project window and source files opening in individual windows. It isn't impossible to add configuration files so that Xcode 3 works with the newer compilers, and if you're using external build systems there shouldn't be any issues at all.
Do I understand correctly that an XCode 3 install isn't touched when upgrading from 10.6 to 10.9?