The question would then be, after the US got a central bank, have the recessions got less severe? The Great Depression was arguably greater than any of those prior to 1913.
Not sure how you weight the great depression, but I believe* the period after the great depression through the 2008 financial crisis featured less severe business cycles than prior to the central bank. The repeated crashes of the late 19th century really were very severe.
In the 19th century, a panic in the US was limited to the US - it was still a peripheral economy compared to Europe. After WWI, the US had most of the gold reserves in the World, Europe was riddled with debt (to the US) and very slow to recover. The Great Depression was greater because it affected the whole World, given the centrality the US had assumed in World trade.
But, more importantly, between the Great Depression and the last crisis of 2008, the Western World never saw any panic as big as those of the 19th century: the Fed had learned much better how to be the World banker, and the US had learned that, after winning a war, rebuilding international trade was much important than collecting war debts.
See also: https://en.wikipedia.org/wiki/Great_Moderation (though that's a shorter period).
* I know a little about this, but not that much. Take what I say with a big grain of salt.