if in doubt use the two of them at the same time, no harm as long as you dont run them at the same time.
To stop spyware cookies in the first place, just edit your cookie handling to accept first party, prompt third party and allow session cookies. When you go to a web site that plants 3rd party cookies you get a prompt and look at the web address. If its not for the site your on, block it always. Over time using this you will notice less spyware being picked up by Ad-aware and other scanners.
its a pain at first, but stick with it and you'll be happy with the result