Let's start with the assumption that Safety is never in the balance. Safety has to be taken into account for any method that we use and that means that we want to keep any food that is time and temperature sensitive out of the danger zone. The danger zone is the temperature range from 40 degrees F to 140 degrees F.
If you have plenty of time, letting the turkey defrost in the refrigerator is safest and easiest, since there is little that you have to do. The turkey is always out of the danger zone and all you have to do is put it in the refrigerator. However, it can take a very long time, 24 hours for each 5 pounds of turkey weight...4 days for a 20 pound turkey.
Assuming you haven't planned that far ahead, the other safe method is to defrost in the sink with cold running water. The water doesn't need to be pouring out, just a steady stream so the water turns over regularly. Water is a better conductor of heat than air, so the turkey will defrost more rapidly than in the refrigerator.
The danger zone is why you don't want to defrost the turkey using warm water, or just sitting on the counter. In either of those cases, the outside meat is warmed into the danger zone before the inside defrosts, so you have some of the meat (the part that is most likely to have come into contact with contaminants) in a temperature range that promotes bacterial growth.