What are the pros and cons of each? Which is better maintained? Which allows for more functionality? Which utilizes the hardware more efficiently? Etc.
OpenKinect is a community of people, not a library. The OpenKinect community releases the libfreenect Kinect driver. libfreenect and OpenNI+SensorKinect are two competing, opensource libraries/drivers. libfreenect (Apache 2.0 or GPLv2) derives from the initial, reverse-engineered/hacked Kinect driver whereas OpenNI+SensorKinect is derived from open sourced (LGPL) PrimeSense code.
Both projects work on Windows, Linux (Ubuntu), and Mac OS X. Both projects allow you to access color and depth images from the camera. The projects are not compatible and they can not be used simultaneously.
Differences between the libraries are motor control (libfreenect has it, OpenNI+SensorKinect doesn't), and integration with the NITE middleware for higher-level NUI support (OpenNI+SensorKinect only). These differences tend to drive projects towards one of the libraries.