Moab is famous as a mecca for mountain bikers rather than trail runners. But any trail that can be cycled can be run. I went out for a couple of runs on the famed slick rock that makes up many of the trails in the area.
My first slick rock experience was in Canyonlands National Park, running a trail that involved a combination of slick rock and sand. Since traversing slick rock leaves no visible trail as it does on dirt or sand, the trail was marked by a series of rock cairns (piles of rocks). Upon reaching a cairn it would be necessary to locate the next one and run towards that. The trail I followed was a well-marked one but even still it is occasionally difficult to locate the next marker, particularly at a running pace.
The other interesting part about running on slick rock is that it is no softer than running on roads. I normally consider trail running as having less impact on the joints (due to the softer surface), but requiring more work from the muscles (since more energy is absorbed by the surface). Therefore running on slick rock surfaces has the impact of road running but requires the concentration and focus of trail running.
When plotting out my run along the Poison Spider Trail, a trail well used by both mountain bikers and jeeps, I was concerned about being able to follow my planned route after reading about some tricky intersections to negotiate. Unfortunately Google Maps only provided limited assistance by mapping only the first section of the trail. But amazingly enough I was able to map out the entire 10-mile section of trail that I would follow based on a photo taken by a satellite. There was enough rubber left on the slick rock from all of the mountain bikes and jeeps that used the trail that a black trail was visible from space.
I read an article about trail running in Moab that said a trail runner would be sold on the area after their very first run. For me I would take a decent trail through a forest over a great trail over slick rock. Running on a soft trail surface through trees is the ideal trail running for me.
I have fond memories of trails through temperate rainforest in Washington State, stunning sea views while running through the forest along the southern coast of South Africa, and great swathes of gum forest in Australia. If picking a location purely for its trail running I would definitely select any of those over the slick rock of Moab.