With tires, it's all about balancing the Power/Weight/Tire combination. A bit more power than traction for Exhibition (lower power to weight ratio, and thus would use one of the N tires to make up for it). For "drift racing", a bit more traction is needed, so utilizing a stickier tire (sports, or low level S), while raising the power to weight ratio, should give you the results you desire.
There is no "Right" tire for any style of drifting. You have to choose your tires based on the 3 characteristics listed above. Then adjust the formula depending on how much (or how little) traction is desired, and how much (or how little) speed is desired.
For any other discussion on this topic, check out the link Loon listed in the above post.