This is not an analogous situation as Euros are issued under the authority of a central government. That was not the case in the U.S. in the 1840's.
The paper notes circulating in the U.S. in the 1840's were not issued by the authority of the U.S. Federal Government. The U.S. Government issued paper money for the first time during the Civil War.
In the 1840's the paper money was issued by hundreds of local state-chartered, private banks. Naturally, some banks were deemed to be, and actually were, safer than others.
Beautiful bank notes Polybius. I love seeing examples of tangible history.
Ditto on the bank notes. Sort of interesting based on what you posted and some I found via google these notes seemed to have pretty ladies on them. Sex sold even in Victorian times. ;)