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.
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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 craftsperson 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.