For me, the most interesting question in the 'what if' game is would the Americans still have their love affair with guns?
A peaceful separation would have meant no overriding need for militias which might have meant that there would be little reason to have a second amendment entrenching guns so firmly into the cultural makeup of the country. It is also possible that the wild west era with frequent conflicts with natives and squabbles with various other countries/colonies to the north, south, and east might have ensured that America kept on loving guns.