darth_ender said:

But I do feel that at the present, CGI still lacks some of the realism of puppetry (while obviously excelling it in some aspects). That is why I prefer a sort of hybrid, with the puppet forming the basis and the CGI simply improving without replacing.

The word you're looking for is "gravity". A lot of the CG creature work out there doesn't correctly - or at least doesn't completely - address how a body and related surfaces move and react to each other. There are so many subtle things that happen with surface density, material weight, force of impact and substance pliability that both the CG animation programming and animator's manual adjustments have yet to completely account for. Granted, some of it is purposely ignored in the interests of giving an action sequence more impact and "wow" factor but there's plenty more where it's not done simply out of laziness or because the people involved simply don't have a good eye for what it should look like. There are so many things that your brain picks up on a subconscious level as to whether an object is real or not that CG hasn't completely accounted for yet.