Squirrel,
Thereis no contest, wheels take it every time for most ground operations, especially running landings and autos. The only advantage of skids is obvious and important, especially for light helos, they are cheap, light and simple. Otherwise, skids are a pretty poor but acceptable:
1) Running landings. Skids are troublesome, as there is really no control over your motion, just some uncontrollable friction. No brakes, and no steering. Wheels provide all that, and also have the ability to move for miles without wearing out.
2) Ground movement. Wheels allow taxi operations with very little rotor wash. Skids require hover liftoff for everything. By about 10,000 lbs, hovering helos are simply painful.
3) Broken ground. A tricycle gear wheel configuration fits almost everywhere, including broken rocky terrain. Skids require that two parallel straight surfaces be found before the aircraft can be landed, let alone shut down.
4) Maintenance. Skids are dirt simple, and take the prize.
5) Weight. Skids are very light, and also cheap to manufacture.
6) Crash attenuation. Generally, wheels and struts are easier to make crash absorbant, but skids can also be made acceptable. Most skid helos are ancient designs, made before crash absorbtion was considered.