Hmm....
It depends.
For one, it depends on the player. Arthur (in my playthroughs) is extremely skilled with any weapon that I personally acquired.
Personally, Arthur would win due to the fact that he's more experienced and is easily adaptable with using different weaponry, but I feel like John (even in RDR2) could easily beat him in a gunfight (5/10). Honestly, I would say it's a tie between who would win. The win could come in a lucky shot.
Mainly everyone will John in RDR1 would win and having played the RDR1 game and watched all of the cutscenes, John is more deadlier with a gun and has killed various bad guys rapidly with one bullet in either the head or chest without missing any shots.
If you were talking about H2H, Arthur would win, 9/10.