"Puppetry" is a very, very broad art form, it encompasses claymation, marionettes, animatronics, stop-motion and a load of other stuff I'm too lazy to list right now. I'm more for puppetry mostly because I grew up on Aardman, I love the movie Coraline and Nightmare Before Christmas and I've always been a fan of animatronics used in the likes of many Spielberg movies and many other classics like The Thing, Evil Dead, Jason And The Argonauts and Tremors.
CGI is also very broad, but I'm more in support of puppetry simply because it seems to be a dying art form in movies today and I don't want to see good craftsmanship being superseded by digital methods. They're both great in their own right and they both have their own utility, so I just hope that CGI doesn't dominate the vista completely as that would be a shame.