I just wanted to drag up this thread again, as I have a few opinions on this sort of thing - particularly as I work in the visual effects field. I used to work for a major post-production company in London who specialse in high-end visual effects for film and television.
We we called to produce a talking snake (voiced by Steve Coogan) for a Miramax film which initially started off as an animatronic puppet. However, the tests revealed that it just didn't look right and was given to us to produce a fully CG version. It worked very well indeed.
Likewise, for Harry Potter and the Prisoner of Azkaban, there were animatronic puppets which were replaced by fully realised CG because, quite frankly, they didn't stand up to the job that the director wanted.
For commercials we've had to replace puppets because the performance required just did not meet the needs of the client and consequently CG models were used instead.
Here's why directors like CG: Whereas with an animatronic puppet, once the design has been agreed upon and everything has been built and tested - it is VERY expensive and time consuming to make any changes without possibility having to rebuild everything again. With CG, you can go in and refine the look of the character AND the performance.
The tools to build, manipulate and integrate these characters into films and TV shows have come on leaps and bounds and I have been very proud to work for a company whose CG character department has done very well. Their latest work can be seen in the form of Reepicheap from the new Chronicles of Narnia film.
Of course, the downside to CG characters is how do you provide feedback to the actor? Well, there are a number of different ways - but ultimately the actor has to work harder to create the illusion whereas having a physical puppet and performace there and then on-set would help enormously.
Also, the number of staff required for a CG character increases (producers, technical directors, character riggers, animators, compositors, system engineers, etc) as does cost.
Many of the ex-JHCS staff have moved to different post-houses around Soho and I've had many interesting conversations with some of them about CG technology and puppetry. NVIDIA have produced some very nice tools for real-time GPU rendering which could make very high quality CG character models for live performances (or on set feedback) much more of a reality than it is now.
It's a shame JHCS closed down, but from what I hear they were expensive and the post-industry was extremely competitive (in fact, it still is).