I have a lot of experience with flintlocks and caplocks, so I would have a bit of an advantage with an old-fashioned dueling pistol. I also own both semi-auto and revolver pistols. No matter what the weapon, I have some experience with it.
On the other hand, my eyesight keeps getting worse and worse as I age, and, more importantly, I have never shot at anything that could shoot back at me. I’m sure that the stress factor of the possibility of death would be a major factor for me.
Flintlocks, for most of their history, were hand made. It wasn’t until the 1800s that they started to be produced using more modern assembly line types of methods. When you need to hand-build a crap-ton of weapons for an entire army, you make fairly crappy weapons. They were smooth bore, as soldiers didn’t have the time on the battlefield to clean their barrels between shots. They tended to use undersized balls, partly so that they could be loaded quickly even when the barrel was fouled with powder residue (which happened quickly with black powder) and partly due to inconsistent barrel sizes. One easy way to tell an antique from a modern reproduction (aside from the obvious aging) is that the real antique will have marks on it from where things didn’t fit properly and were roughly hammered or filed into working order. Quality and fit were very inconsistent.
Dueling pistols weren’t so hastily made. Many of the ones that I have seen have had rifled barrels. After all, if you are only firing one shot, barrel fouling isn’t exactly an issue. Even if it’s a smooth bore, using a tighter fitting ball can dramatically increase the weapon’s accuracy. Again, the reason to use an undersized ball is to deal with barrel fouling, which isn’t an issue in a single shot weapon.
Dueling pistols also tended to be well-maintained. A poorly maintained flintlock will often just click when you pull the trigger. If you keep it spotlessly clean and keep the flint properly napped, the weapon will fire almost every time (unless it’s wet - flintlocks in the rain just go click).
At dueling distances, I wouldn’t call an antique dueling pistol a “crappy” weapon. They are quite deadly and accurate at those ranges. Smooth bores do pretty much always fire curve balls, but they’ll go straight enough over the distance of a typical duel.
Dueling started to fall out of favor in the mid to late 1700s. Many considered fighting to the death to be brutal and uncivilized. There started to be a growing sense that a proper gentleman should be able to resolve his issues without resorting to violence.
By the time of the Burr-Hamilton duel, Burr ended up being charged with murder, though the charges were dropped before going to trial. The duel ended Burr’s political career.