FrogReaver
The most respectful and polite poster ever
Good points.
1. There's no way for me to model the entire party. However adding more people fighting the same mob drastically reduces the difference in kill time between one-handed and two-handed weapons, and the higher AC gains much more prominence and value.
2. Yeah, duelist shifts things in favor of one-handed, but then great weapon fighting shifts things in favor of two-handed. Which one you took will certainly shift things in that weapon's favor.
Let's assume one-handed vs two-handed longsword, with 1d8 vs 1d10, and 16 Str. 7.5-9.5 damage for 1H; 8.5-9.5 for 2H. Rerolling 1s and 2s gives an overall boost to average damage of about +1.
Closer than I was thinking... Oh, right, I was using 1d6 weapons for 1H before, which would give 6.5-8.5. Depending on which 1H and 2H weapons you're considering, and which fighting style you're using, the shift could be anywhere from +60% (1d6 → 1d12/GWF) to -10% (1d8/Duel → 1d10) So that can definitely impact the overall results.
As far as consistently killing in 3 hits vs 2, that was only the baseline that assumed 100% accuracy. Once accuracy was applied, it was more like 4.5 rounds to 3. And if comparing the longsword switch-up while having the Duelist fighting style, one-handed will be better. It would be roughly the same as the 1d12 greataxe. Of course, if you're using Great Weapon Fighting, the two-handed versions will be notably better, at 25% (2H longsword) to 40% (greataxe) ahead.
All told, the one-handed longsword with Duelist style and a shield is probably your best combination. You're doing comparable damage to the two-handed weapons, but with a higher AC. GWF greataxe is only around 10% better than Duelist 1H longsword, which shifts survivability strongly in favor of the higher AC.
3. At 1st level, where two hits can kill, and ignoring crits, which are pretty much auto-kill in themselves, looking at the odds of taking two hits in N rounds with a 2 AC difference and no healing:
1 round: 0%
2 rounds: 16% @ 16 AC, 9% @ 18 AC
3 rounds: 35% @ 16 AC, 22% @ 18 AC
4 rounds: 52% @ 16 AC, 35% @ 18 AC
5 rounds: 66% @ 16 AC, 47% @ 18 AC
An extra 2 AC provides a fairly substantial improvement in your odds of surviving. 1 in 2 with an 18 AC would survive 5 rounds, while only 1 in 3 with a 16 AC would.
Another consideration is that many classes have damage upping abilities that don't depend on weapon size. Barbarian rage damage. Paladin Smites. Ranger's hunter's mark. Ranger Hunter's colossus slayer. Battlemaster Superiority Dice. Many cleric subclasses get a melee scaling damage bonus. These abilities further lower the percent damage differences between big two handed weapons and smaller one handed weapons.
All in all it's a complex problem. On classes that get bonus damage independent of weapon size I tend to like sword and shield much better than two handed. On barbarians I tend to like two handed weapons better. All in all I would tend toward sword and shield alot more if it wasn't for the -5/+10 feats or polearm master or crossbow expertise.