Why don't you test it yourself. There are many advantages and disadvantages of each software. I was also a fan of Bitdefender before, since it slowed my PC and it was buggy I have to get a good alternative. So in ur case if every thing is fine between the two then i would suggest to opt Bitdefender over AdAware .
I personally do not like either one.
BitDefender's statement of "
BitDefender Antivirus Free Edition uses an intelligent mechanism that can automatically take the optimum decisions to provide ironclad security without slowing down your computer." is rather an understatement. On my time using it, it did slow down the system and it was a mid range system.
Lavasoft's free solution's statements of "Fast Antivirus" is also an understatement, at least since I last used it back in November.
They also have questionable RT and Web Browser protection.
If you take the performance question away and focus on protection/modules, then BitDefender is ahead, but I would still not recommend either one.
If you think that Adaware has AVC (ActiveVırusControl) you are wrong AdAware Pro Antivırus has AVC, their free version has not proactive defence against zero-days.
Bitdefender Free is better than AdAware Free antivirus.
On the other hand, there are better options on free antivırus market. These 2 are the latest option which I will consider.
For me I will go from Bitdefender in this case but if I'm not mistaken Ad-Aware has been license to use the engine from BD or Vipre? Not sure about this but again it will differ from own engine implement.