There are two main components of a rivalry: familiarity of the opponent and relative parity. This generally makes someone from within your division the most obvious choice as a chief rival. Seeing as if it weren't for Deadpool, no one in St. Louis would even know how to pronounce Regina, the main rivals of the Crows is Detroit.

In many ways, Detroit and St. Louis are similar cities. Both are major midwestern cities with something of an inferiority complex. They don't receive the recognition the American public generally reserves for the coastal cities, and even within the midwest they are both overshadowed by Chicago. That, however, is where the similarities end. Take, for example, the best known local foods. Detroit is best known culinarily for Detroit-style pizza, which in itself, is a microcosm of Detroit as a city. It is far less renowned than both New York and Chicago style pizza, yet similarly polarizes people into love-it or hate-it camps like Chicago style does. Only, it's just a watered down version in every way: less well known, less ubiquitous, and really, its more of a like-it or don't-like-it camp. Jon Stewart will never go on a Detroit style pizza rant, and no one will write articles extolling the virtues of Detroit pizza as the best in the world.

St. Louis, on the other hand, has St. Louis style ribs. Unlike Detroit pizza, this is universally acknowledged as best in its class. They have the most flavor of any rib cut, are by far the most presentable, and are considerably cheaper than the vastly over-rated baby back rib.

I could go on about other ways St. Louis is superior to Detroit, such as how the most famous landmark in St. Louis is the totally dope Gateway Arch, while Detroit has, uh.... car factories I guess (yay industrialization!), but it gets kinda mean. The point is, Detroit is St. Louis rival and it will likely remain that way for all time.