I have heard multiple times in this thread that the Battlemaster Archetype would heavily favor TWFs, because of the extra attack. Having not seen the Battlemaster Archetype, I could not argue otherwise. However, I now have the player's handbook and have had a very close look at it. Needless to say, I did not find Battlemaster to heavily favor TWF except at low levels. Given that TWF has the higher DPR at low levels, it just seems to make a TWF even more powerful in that range, but the advantages rapidly evaporate at higher levels. Let me detail my analysis.
1. A Battlemaster gets 4 superiority dice to start at level 3, has 4 at level 7, and 6 at level 15. He can gain an extra die by taking the feat for a total of 7 by level 15. These reset with a short or long rest.
Analysis: This would tend to limit the advantage of going TWF. In small amounts, these are likely to be used whether you use a single weapon or two weapons. It really depends on how often you get a short rest to reset them. The TWF is more likely to get the "on-hit" maneuvers off when he wants them off since he would have two hits to one at low levels, but this advantage will be minimized as I will show.
2. Maneuvers effects themselves.
8 of the 16 maneuvers are "on hit."
2 maneuvers use up your bonus action, Commander's Strike and Rally.
2 maneuvers, Parry and Evasive Footwork, are bonuses to AC.
2 maneuvers, Feinting Attack and Precision Attack, increase your chance of landing a single attack.
1 maneuver, riposte, allows you to use your reaction to attack.
1 maneuver, lunging strike, extends your range.These are the ones
Analysis: I am going to start backwards.
-Lunging, riposte, feinting, and precision attacks favor Great Weapons since the focus is on a single attack and those hit harder.
-Bonuses to AC effect all styles the same. Parry may favor TWF over great weapons if the TWF is Dex based. Duelist could be Dex based as well and gain same benefit.
-Commander's and Rally eat up your bonus action, reducing TWF damage down to a greater degree than the other styles.
-The 8 on hit maneuvers favor TWF because of the extra attack. Let me show by how much. This advantage deteriorates right along with DPR as you level.
Chance to get a hit in a single turn at 60%(not counting OA's)
Level 1
Single weapon - 60% (1 attack)
TWF - 84% (2 attacks)
Level 5
Single Weapon - 84% (2 attacks)
TWF - 93.6% (3 attacks)
Level 11
Single Weapon - 93.6% (3 attacks)
TWF - 97.44%
Level 20
Single Weapon - 97.44% (4 attacks)
TWF - 98.77% (5 attacks)
Add in an OA, and the gaps closes even more.
Conclusion - Battlemaster "on hit" maneuvers heavily favor the TWF at low levels due to greater control of when you land you maneuvers. This advantage deteriorates heavily by level 5, and is negligible by level 11. The lmit on the number maneuvers means all styles gain the same DPR benefit and two maneuvers are likely outright avoid at all costs for a TWF. Battlemaster is a balanced Archetype for the all the styles from level 5 on in my opinion, which is only dissappointing because Champion heavily favors GWFs, and Eldritch Knight really sticks it specifically to the TWF with the War Magic feature offering an extra attack that a TWF would have anyways, not mention spells that would eat up the bonus action as well.