According to Scientific American (February 2009), ion engines start off slow, but build up speed as they travel. At what travel distance would an ion engine (such as an ion thruster, a Hall thruster, or a magnetoplasmadynamic thruster) be faster and/or more efficient than conventional (solid/liquid) fuel engines.
At the risk of not answering your question directly, I will suggest to you that you consider two other, better figures of merit for propulsive efficiency than distance and speed: specific impulse and thrust. These two measures are more meaningful because they impact the key hurdle in space travel: energy. A good illustration of this is available here. Notice how the Moon and Mars are about the same energy-distance from LEO.
Two points in space may be far apart but require very little energy to move between. Conversely, two points in space may be relatively close but require a large amount of energy to move between.
Chemical rockets will probably always provide higher thrust and ion engines will probably always provide higher specific impulse. These measures then usually map into transit time and mass efficiency. If you must have a fast transit time, chemical rockets will usually win up to the practical limit imposed by the rocket equation and Hohmann transfer orbits. From then on, it is all ion drive and slow, spiraling trajectories.