No, do not run both applications together. Both will attempt to decrypt and you will likely experience conflicts.
AnyDVD is a driver that runs in the background and works well with a variety of software, such as
nero, etc.
DVDFab (Express, Gold or Platinum) is a complete program and will copy a copy-protected dvd (ie., rip and burn). DVDFab Decrypter (freeware) will rip a movie, but you must then use a burn application such as nero, DVD Decrypter, Img, etc.
Hope this helps...