There's something about a leather saddle that it gives just the right amount of hardness for comfortable riding. A softer saddle cuts off circulation over a larger part of the body, which leads to discomfort. A harder saddle localizes the pressure too much, creating discomfort at two spots.

Aside from that, leather breathes. I think that's more important than the hardness issue. Since the leather breathes, it keeps you relatively cool and not particularly sweaty.

But the biggest payoff is on long rides. I can ride a few miles on any saddle, and it really doesn't matter much. For fifty or a hundred miles, leather is much better.