No, not better..just different. DVDFab is an all in one program that can decrypt/rip/compress and burn to a single layer dvd. Another strong point is that it is updated quite regularly.
AnyDVD runs in the background and breaks encryption. You can use it in combination with other tools...I like the free ones, DVDShrink and DVD Rebuilder. AnyDVD also has a built in ripping engine, so you can use it to put the entire movie on the hard drive and work with it from there. But AnyDVD has no native compression abilities, and no way to burn by itself. I use a great, free burning program called ImgBurn for that.
AnyDVD is updated just as quickly, sometimes even faster, than DVDFab.
Both are good tools. I just prefer AnyDVD. I have the HD version of AnyDVD which will rip blu ray.
And for any regular dvd that requires a lot of compression, I use DVD Rebuilder Pro, which uses an mpeg2 encoder rather than the transcoders seen in DVDFab or DVDShrink. It is slower, but produces higher quality output.