The original Constellation would have been close enough to the Constitution to be considered a "sister ship." The Constellation in Boston Harbor was a sloop-of-war of 23 guns. Constitution and (if I recall correctly) the original Constellation from the 1790's both carried 44 guns.
During the unpleasantness around 1812, certain British naval officers complained that they were actually 64 gun ships-of-the-line with the upper deck removed. (Which possibly explains the complaints by some of the folk here.)
Properly handled, they could fight nigh-on anything up to a 4th Rate ship.
Superior frigate design was nullified after Napoleon surrendered and the large numbers of Royal Navy ships (and sloops and brigs and cutters) were able to coming by for a wee visit... off the coast of the US.
The fragment could indeed be genuine. I know of know claims of miraculous abilities on it other than an aversion to British solid, canister and grape shot.