It is mainly the Windows Defender (WD) which comes pre-installed in win8 that you have to worry about as that version of WD is an anti-virus also, which is closer to MSE than the old WD installed with win7 (I can't comment about vista, never used it). However when you install another AV in win8 it is meant to disable WD.
The thing that I hated most about win7 was the inability to completely uninstall WD only to disable it as it isn't disabled when you install an anti-virus. Personally I see little point in having WD enabled when you have avast installed, if you want something else as a compliment to avast, then MBAM is a good companion and the MBAM pro version (one off license fee) even better.