Convenience: The best way to think about this problem is to remember that the more convenient a grill becomes the less smoke flavor it produces. An electric grill is the easiest to use, but doesn't have that real fire flavor, while hardwood fires give you the best flavor, they are the hardest to deal with.
Authenticity: The authentic smoky, off the fire taste of grilled foods is strongest with the original heat source, wood. As you move to electric units, there is very little of this flavor left. In fact, many electric grills add virtually nothing to the taste of foods. However, the simplicity of flipping a switch and grilling, can't be beat.
Taste: On the subject of taste, a study conducted a while back, participants were presented with hamburgers and steak cooked on gas and charcoal units. No one could tell the difference between the charcoal or gas when it came to the hamburgers, but they could tell the difference with the steak. The charcoal grilled steak had a distinct smoke flavor.
Space: To decide what kind of grill is right for you, consider where the grill is going to sit. A small patio or covered area is not the place for a large charcoal grill. Electric grills produce no flare-ups and are safer in smaller areas. Gas grills do produce flare-ups and need to be away from any structure to avoid those pesky house fires. Charcoal can be lit with an electric starter and therefore, used with virtually no open flame.
Grilling: Another thing to consider is how you plan to grill. If you want to come home from work and throw a couple of steaks or chicken breasts on the grill with virtually no hassle, then an electric or gas unit might be what you are looking for.
Cost: Finally, there is the issue of cost. Gas grills are generally more expensive than electric or charcoal; charcoal being the cheapest. If you don't want to spend a lot of money then charcoal might be the answer. However, charcoal is the more expensive fuel. You can easily spend $5.00USD a cookout on charcoal, while gas might cost around $.20USD per cookout. Charcoal won't save you money in the long run.