The Dukes of Hazzard is one that pops to mind immediately, Shrink wouldn't touch it, DVDD no problem. Actually there are many that Shrink can't muster due to it's inactivity of about 3 years, DVDD has not been updated for a little over a year. Shrink is a great program though, as you know, it's only fault is it's outdated ripper, which as you've said will work fine with AnyDVD, DVD43 etc.
As far as putting the movie on your HDD, it's useful if you use different programs. I use CloneDVD2, DVDFabGold, DVDShrink, & DVDRemakePro on a very regular basis, if you have it on your HDD, you'll not only save time, but it is also easier/faster to edit content from the HDD than the disc. I'll often make a movie only backup, and also a 2 disc split with no compression of the same movie. On another note, Shrink does not do a good job of handling dual layer burns(ie layer break placement), where an ISO read from DVDD and then burn it with ImgBurn is arguably the most fool-proof method out there.