AdAware and avast are two entirely different beasts and do different things, avast isn't interested in cookies, etc.
avast! is primarily an anti-virus and whilst you might not have any viruses adaware could pick up non-virus cookies, stuff to deliver adverts, etc. that avast isn't going to detect.
Having opened the simple user interface, the grey window (the Simple User Interface) with the big play (start) button.
You need to select Local Disks to be able to have selected scan archive files, you also have different Scanner sensitivity settings, Quick (slider to the left), Standard (slider in the centre) and Through (slider to the right). Thorough as the name suggests is very through and can take an extremely long time. The best setting I feel is a Standard scan without archives, this gives a good balance between performance and protection.
Archive (zip, etc.) files are by their nature are inert, you need to extract the files and then you have to run them to be a threat. Long before that happens avast's Standard Shield should have scanned them and before an executable is run that is scanned. Thorough is also by its design very thorough and perhaps a little overkill for routine use, were a Standard scan without archives should be adequate.
I have only ever done a through scan with archives once shortly after installation just to ensure a clean start state, but with XP for example avast will do a boot-time scan after installation if you select it, this I believe will be quicker and reasonably effective. Like everything in life things are a compromise.
