I'd have to say that the revolver, rather than the autopistol, is the quintessential American firearm. From the Colt Paterson, through all the front-stuffers, to the SAA, through the S&W M&P, right up to today's highest-powered handguns - all revolvers. The 1911 is a wonderful firearm, and is very American, sure, but I submit that it's not the same as the revolver.
As to which revolver, I don't know that this is all that important. The single-action designs dominated the 19th century, culminating in the SAA. The double-action designs dominated the 20th century, with the S&W unquestionably the champion here (as evidenced by all the S&W copies in South America, Spain, etc.). I'd accept either one as the exemplar weapon of America. The SAA has the historical cachet, but in sheer numbers, the S&W dominates the scene, particularly for the last century.