Reading through the posts every has made some good observations. One thing that is not mentioned is that horse has a higher natural oil content. This combined with the tighter grain contribute to the moisture resistent properties of the hide. It is not water proof.
The horse hides I use are the same thickness as the cowhides.
Both hides block well and retain that shape.
Both are long lasting with proper care.
Horsehide resists salt staining from sweat.
Horsehide will break in faster.
I have not experienced any problems with uneven coloring of the hide.
If you wear your gun for extended periods where you are subject to periods of heavy physical activity or if you prespire heavily choose horse. For all other, cow will serve you well.