As with many things in golf, this is not an either/or proposition. Both areas have to be in sync for the desired results to occur. The fastest clubhead speed in the world won't do much for your distance (or ego) if it isn't accompanied with proper clubface contact. And likewise, the best contact won't do any good for distance if there is no speed on the clubhead. In order to acheive distance, you need both.

Clubhead speed is controlled by a number of factors and they all need to be working together to get the results you want. The most important factors to remember are:

The speed of the body rotation
The speed of the arm swing
The speed and timing of the hand release

Your leg drive determines the speed of the body rotation, which determines the speed of the arm swing. Proper focus and relaxed arm and hand muscles determine the timing and speed of the release.

Turning the legs and hips toward the target will initiate the arm swing and fast loose hands complete this integrated system of movement. The legs are the only part of the motion where strength is critical. The muscles of the upper body should be transmitters NOT generators. This is why even smaller players can punch out a long distance shot as compared to larger, stronger players. The strength in your arms plays little past in gettnig that clubhead up to speed.

In fact, those stronger players who feel as if they can just muscle their way through are often disappointed. Don't let that happen to you.

Lastly, when you swing, use about 80% of your strength. Anything above that and you're probably going to be losing distance rather than gaining it.