After running two 10k races and one 5k at KI, I realized each experience varied wildly. All were fun. Different partnering groups combined with other administrative limitations like time of day and the season have an influence on the experience.
Early Morning Races - If a race is planned for the early morning, before the park opens its gates, the run has more freedom to enter operational, on stage (to borrow a term from Disney, which was borrowed from the theater,) areas of the park. These events are usually the longer runs, in the 10k and half-marathon distance.
It is very special to run along the same paths that are usually crowded with people and filled with the noice of rides and music. There may be fog and a pretty sunrise along the way. There is a down-side too. The park smells, like food and also garbage cans and garbage collection areas might be catastrophic for a runner who may have a fragile digestive system. I've run under the racer, where it passes through to Flight of Fear and Firehawk. That is near the garbage processing and nearly lost my breakfast.
Likely, the path will also extend beyond the park and allow you to run along several service roads. This another special treat for serious fans of the park. You can see what normally can't be seen by park visitors. The backside of The Beast is spectacular! It looks like an enormous wooden barrel. There are braces all along the outside of it, which help keep the cars from hurtling off into the woods. Different service areas change over the years. Once, I saw a "bone yard" of old props. There was a large scale Sponge Bob recognizable among the heap. I also ran past the Red and Blue trains of the Son of Beast, which were parked beneath its structure before it was torn down.
Evening Races - There are usually short 5k and sometimes kids races planned during park operating hours. These certainly can cover a lot of the same off stage areas described previously. Howver, if the park is open you can be almost certain that your running path won't mix with the crowds and on stage areas. The recent Halloween Haunt's 5k Glow Run was one of these events. The path began on the east side of the parking lot and entered the service roads near Invertigo. If watching it on a map, it meandered clockwise around action zone, up along the back of Coney Mall. It followed a small portion of the Dinosaur path and then went towards The Beast, finishing in Soak City, which was closed for the season.
So when you select the run, pay attention to the features they say you get to explore. Sometimes you can view a map of the planned couses. There may be competitive runners that blow past everyone in the beginning of the race. The greatest benefit, in this author's opinion, is the opportunity to explore behind-the-scenes paths, venturing safely into areas normally off-limits. These are areas that offer unusual views of many of your favorite attractions.
Photo illustration by Mike Kunze, source photo credits: Runners in a 5k - Creative Commons Attribution 2.0 Generic, Diamondback - Public Domain, Kings Island Eiffel Tower - Creative Commons Attribution 2.5