I know both words share the same meaning and pronunciation, but I wonder about their comparative usage in modern English.
Google Ngram Viewer (for the "British English" corpus) shows that gaol was more popular than jail until the mid-19th century, that the two words were used with broadly similar frequency from then until the mid-20th century, and that now jail is the most common spelling.
However, if you look at the actual citations you'll see that recent uses of gaol are largely in historical contexts (for example, historical studies of gaol records, or reprints of works like The Ballad of Reading Gaol) so that Ngram Viewer underestimates the modern dominance of jail.
It might be interesting to know that the British spelling shows the French origin of the word; gaol is derived from French la geôle. I would not say the American spelling is a corruption, it is a logic simplification of a very difficult spelling and renders the pronunciation. That may be the cause that jail is slowly gaining ground over the historical, but difficult spelling gaol.