Why can a cow eat large amounts of hay and a pig can't?

For one, cows are much bigger than pigs and thus have larger stomachs.

Two, cows are able to digest a lot of hay much more efficiently than pigs can.

Three, the digestiive systems are different between a cow and a pig. Cows are fore-gut fermentors or ruminants. Pigs are monogastrics. Fore-gut fermentors are built to digest roughages like forages, where as monogastrics are built to digest a diet high in starches, protein and carbohydrates much more efficiently (without getting sick) than cows.

Four, cows love hay. Pigs don't, and they normally wouldn't even touch the stuff.