Benefits of Titanium
Titanium shafts have great strength and they are also on the stiff side. This is good for stronger golfers who have no trouble getting distance on their shots but may be concerned with accuracy. The stiffer shafts will keep the ball from straying off course--as long as it is aimed correctly--and golfers will get power from being able to generate the titanium shafts with enough speed and then snapping their right hand at impact. The key to being able to use the titanium shafts successfully is having enough strength to swing the clubs.
Benefits of Graphite
The advantage of graphite shafts (which is really graphite combined with titanium) is that it is much lighter than titanium and therefore easier to swing. The lighter nature of the clubs also enable the manufacturers to move much of the weight in the clubs' head back further, which makes the clubs more forgiving. Graphite shaft clubs may be for you if you are a relatively accurate hitter but lack the distance you want on most of your shots. Graphite shafts are also good for older golfers who may not generate the club head speed they once did. Many women golfers also like the extra distance they get from the graphite shafts.
Some golfers get turned off to the graphite clubs because of something that is missing--the sound of the club head hitting the ball. When swinging the club well, golfers love to hear the crack of the club face against the golf ball, much the same way baseball fans love to hear the crack of the bat against a baseball. The sound of the club head hitting the ball is more than something that is aesthetically pleasing. It reveals to the golfer whether the swing was a good one. The argument can be made that the shot itself will reveal whether the swing was adequate or not and that is arguably true. However, sound reveals subtle nuances to the golfer that he would not know if he did not here them. The graphite shafts go along way toward dampening that sound to the point where it is very difficult to make out and interpret. For that reason, some golfers prefer the titanium shafts.