DVDx 2.2 is an encoder that will take your original DVD and will actually re-encode an MPEG2 stream to your specifications (ie, defined bitrate, resolution, etc). However, the program's internal encoding engine is not of the highest quality, meaning that it is usually used as a frameserver for TMPGEnc Plus.
I used this program a lot when I was making VCDs and DivX movies, and it is excellent at what it does and very intuitive. If you want to use it to produce DVD compatible streams, I suggest you head over and check out this guide:
http://www.dvdrhelp.com/forum/userguides/129990.php
However. I would suggest that DVDShrink or DVD2One are probably better tools to use if you are simply backing up commercial DVDs.
While re-encoding is generally acknowledged to produce higher quality than compressors (like DVDShrink and DVD2One), there are two things to consider: 1) re-encoding takes a long-time, as long as overnight if you frameserve to TMPGEnc (not including authoring and burning), while compressing takes about 1 hour; and 2) you probably won't notice much quality difference, especially if you compress using the "movie only" method.