Just to clarify the exact mechanics of the Duel...
The important thing to pay attention to are the gauges on the right side of the screen and the Aim Reticle.
The Blue gauge is yours, the Red gauge is the enemy.
You'll notice that when you press fire, the gauge will fill by either small or large amounts (depending on the accuracy of your reticle and the area of the enemy youre hitting).
Every time you press the Fire button, a black line appears after the filling the gauge by a bit (or a lot, read further). Each black line is a bullet and every increment shows how "well" you aimed.
Who wins the Duel is determined by this gauge, not by the amount of rounds you select. I routinely win Duels with only selecting one shot (to the head or gun). So here is a step by step and its explanation...
After the stare down, you can use the Right Stick to put your hand closer to your gun (giving you the jump when it comes time to draw). You can pull first, which gives a small boost to your gauge but in doing so, you incur an accuracy penalty (the reticle cycles quickly). If you wait for your opponent to draw first, you dont get a boost to the gauge but your accuracy is FAR better (the reticle cycles slowly).
What I mean is, the reticle doesnt cycle nearly as fast (from red (inaccurate) to white (accurate), so its easier to paint the target with all accurate shots.
Basically, you can win every draw only painting one target (usually the head or weapon). When you wait for your opponent to draw first, just life the reticle and take your time to line up the shot, select it when its White and watch a one shot, one kill. Your gauge jumps through the roof so long as your shot is accurate and in a proper location.
I farm Fame and Honor by cheating in Poker, getting caught, and being forced to Duel. I then shoot the weapon out of the hands (one accurate shot = Full Gauge) of my opponent, which is +200 Honor and +100 Fame...every single time.
Side note: I figured out Dueling by proxy of trying to learn how to cheat in Poker. Seeing as I physically cannot keep the Cheat gauge out of the red, every time I tried to cheat, I got caught...which meant a Duel, usually with the General Store owner in Armadillo. Killing him in a Duel closes the General Store for 5 days, but worse than that was there now were only 2 guys at the Poker table (less $$$ on the table). SoI kept trying to disarm him in the ensuing Duel and couldnt do it consistently. After many tries and a lot of re-loading, I figured it out.
Just be accurate and pay attention to your gauge...if your first painted target fills your gauge to MAX (it certainly can if done right), just sit back and wait for the DeadEye time to run out, because you won with one shot.