Cowhide is the utility leather, whereas pigskin is a nappier, usually softer leather. Both have advantages and utilities, although for sheer cost and quantity, cowhide is the far more common of the two.
The West and Africa have strong beef industries, so cowhide is a natural and fairly inexpensive byproduct. In Asia, where pork is more of a staple product, pigskin is more common as a byproduct.
When a craftsman requires sheer size in a hide (for example, in upholstering a couch or an automobile), he'll use cowhide. The average steer outweighs the average pig by nearly twice, hence, the much larger skin.
Pigskin is fairly thin but very durable; therefore, it is used as a liner in fine leather goods. Pigskin (and buffalo hide) is a sign of luxury in polo saddles, versus normal cowhide.
Cowhide has a smoother texture, making it suitable for tooling and design work. Pigskin has a dappled texture that is pleasing to the touch but that is unsuitable for tooling.
The American football is called the "pigskin" because it was once made of pigskin; however, modern footballs are made of cowhide.
Letitia Baldridge, in "New Complete Guide to Executive Manners," warns not to give a gift of cowhide leather to a Hindu or a gift of pigskin to a Muslim. The cow is sacred to Hindus, and pig flesh is forbidden by the Qur'an (the holy book of Islam) for either apparel making or consumption.