Ok, I'm seeing a LOT of misinformation in this thread.
1-Handbreak is an app designed to compress movies to a format to watch on your iPod or computer, not burn back to a DVD. You can reconvert the AVI or MP4 file back to DVD, but you are going to lose quality when you do so as nothing that HB encodes is DVD quality, they are ALL lossy formats.
2-Handbrake will not handle DVDs with any serious protection on them, such as "zero cells". You have to use MacTheRipper and DVD2OneX to get around this, but we won't discuss that here as it violates forum policy.
3-Mac the Ripper will simply copy a DVDs Video_TS folder to your Hard Drive.
4-You need Toast or Popcorn to burn that Video_TS folder BACK to a new DVD. This process is lossless and you retain full quality from the original.
If all you want to do is copy a DVD to another DVD, use MacTheRipper. If you want to convert DVDs to watch on your Mac, iPod or eventual AppleTV, then Handbrake is the App for you.