You shouldn't download anything from anywhere. The software disc that came with the Extreme is the latest version you need. The online version is not the latest version and will not work. The version on the disc is AirPort Utility 5.5. The latest online version is 5.4.2 (which does not work with the new Extremes). Anything earlier than 5.5 will not work.
Also, AirPort Admin Utility is the old name for AirPort Utility, so you are indeed downloading an old, deprecated copy of the software you need (which is on the disc).
Edit: While it usually is safe to assume that the online version of a particular software will indeed be the latest version, that's not the case in this situation. Apple has yet to release 5.5 online since the debut of the simultaneous dual band Extreme and Time Capsule.