I love crashing thru the woods on my Gary Fisher rigid hardtail, but something is missing.
There is not a direct connection to the dirt.
Trail running is an intimate affair. Slow speeds (relative to a mt bike) and feet-to-dirt are the main factors for making trail running a different experience as compared to the mt. bike.
With running, especially on a very technical trail, your mind-to-feet sensors are usually at overload status. Your brain is processing thousands of commands within seconds. But at the same time, your brain is also soaking up all of the smells & sights that surround you.
With big tires & full suspensions, the lay of the land is lost for the mt. biker, but not for the trail runner. Since every grain of soil, rock and root is touched upon by your feet, a greater sense of the environment is realized.
Throw on a pair of running shoes, hit the trails and get closer to the dirt (this may even improve your mt biking). And in the process, have tons of fun while running thru the woods (& rivers, etc.).