Cowboy boots have pointed toes that still give plenty of space for the foot. And the reason is actually a very simple one. A pointed toe makes it much easier for the rider to regain a lost stirrup. As stirrups are so essential when roping and working cattle, a cowboy can't afford to keep riding without a stirrup.
Knight's armor boots are pointed for the same reason. English riding boots are not - in most English disciplines, riders can simply carry on with one or no stirrups and not have any problems.
Pointed (and heavily decorated) cowboy boots, courtesy of ZeljkoArtist (Via Wikimedia Commons).