Either one will serve well. The main difference between cow and horse is that horsehide has a tighter grain that makes it stiffer and a bit tougher. It's less susceptible to moisture (sweat, humidity) but it doesn't seem to accept dye very well (which may explain why it's only available in 'natural' color).
I got the horsehide upgrade and it took about 10 days to completely finish breaking in. But then I'm 6'2" and 175 lbs so the leather had to make a pretty tight turn (almost a quarter-circle) when molding to my 3:30 position. Now that it's broken in, however, I don't even know it's there; I have to deliberately bump the gun with my elbow!
Horsehide is nice to have, but cowhide will get the job done just as well.