Most programs in the DVD Shrink category (I don’t know all of them, but if the program offers quick and easy dvd backups, it usually is) use some sort of mathematical trick to change the compression of the dvd. How well this turns out, depends on the source material and on your home cinema setup. On a good quality large screen you will notice the difference more.
DVD Rebuilder uses your choice of encoding modules (free, commercial or trialware) to re-encode the video stream from the original dvd. Depending on your choice, this can take a long time, but the end result is usually a lot better. Most experts agree that the CCE encoding module is the best option. You can set DVD Rebuilder to use 1-10 passes; the more passes, the better the end result will be, but after a certain number of passes the difference will be negligable. I use 2 passes if in a hurry, or 6 passes if I have the time and want the best result.