I think there is a functional difference. From Twinoaks post in the thread I referenced...
The diamond cross section awl is sometimes referred to as a saddler's awl. One reason it's used is that it's pretty strong, and needs to be to push through thick leather. It also (when positioned correctly) presents a 'flat' face for the thread to pull against. This is important because if presented with the corner of the hole, the thread could cut the leather. Having a fairly narrow, but long (when compared to thread diameter) allows easy passage of the needle, but also closes up nicely.
One can argue how much difference it makes, but I think it is clear there is a difference.