Alarm Clock _is_ a "whole application", and resides in the Applications folder. Simply its icon doesn't appear in the Dock (so as not to clutter it), but in the menu bar. You can quit Alarm Clock by selecting "Quit" in the pop-down menu that appears when you click on its icon.

Aurora has a nice name and a good looking interface, and I like that you can just type in the alarm date and time figures. It works pretty well.

Alarm Clock is better in the "interacting-with-iTunes" department (e.g.: the Easy Wake feature is better than it is in Aurora; you can select just the song you want instead of a whole playlist; ...), and its "concept of use" is also easier and quicker to grasp, imho.