I'll try to be brief.
Okay, for our purposes, an encoded picture contains DCT data and motion vector data.
A motion vector is a two-directional pointer indicating changes from previous frame. Motion vectors have half-pel resolution and interpolation is necessary. Motion estimation finds the motion vector giving the best prediction macroblock in a reference frame or field. Blah blah.
The primary purpose of DCT data is error compensation. This is what DVDShrink, hmmm, cuts down on. It can't really lose motion vector data. It has to work with the residual pixel data, the DCT data. All compressed domain transcoders work by dropping DCT coefficients, that is, by requantizing.
So how does all that work out in practice? Here's where the disagreements start.
Say you have an action movie that requires a lot of compression and has a fair amount of dim scenes. The worst thing you can do is use Max Sharp. You've already lost a good bit of DCT data, the result is likely to be slightly jerky. Furthermore, the low ratio guarantees block noise (especially in the dim scenes) and ringing. Max smooth would be a better choice here.
Or how about a "talking head" movie at more modest compression? Max sharp may not be too bad in that case, but probably not worth the extra time.
AEC and Deep Analysis add significantly to transcoding time. For the time required to use AEC, why not just re-encode with something like DVDRebuilder and get the best possible result? Or split the disc. For myself, I never use AEC anymore, and only transcode when the result will be over 90%. YMMV.