I have been reading about the new Cineform Neo, but is it only for certain cameras with specific outputs? I am unsure of exactly what it does, but it seems to be the upgrade from Connect HD?

Neo is software-based, and isn't hardware/connection dependent. However, all of the camcorders that can benefit from Neo have 1394 outputs on them, excepting some of the USB-format AVCHD camcorders.
Neo isn't for a specific camera, but rather a specific codec that can be accessed in various NLE systems. Not only does it preserve the integrity of the original information, but it provides a nice bridge between various applications.

So, am I right believing it is an upgrade to Connect HD, therefore a better codec?

NEO HDV is the grade to Connect HD, and yes it is a better codec, along with many more catpure and conversion features. NEO HD is a 1920x1080 10-bit version of NEO HDV.