I feel like the optimal use of the Battle State buffs now only requires us to stretch out of the duration of BR+BH until Battle-Shout/Valiant Strike/Shadow's Lament comes off of cooldown. Without legacies, IIRC BR and BH each last 8 seconds, while Battle-Shout's cooldown is 15 seconds with no Sure Strike resets.
So, the Battle State Duration legacy isn't strictly necessary to maintain 100% uptime on Battle State buffs. Though, in practical terms, we're probably looking at more like 80-90% uptime.
Now, on the other hand, if you really want to min-max and keep one or the other Battle State buff up at close to 100% uptime, you'll definitely the legacy. You can get your preferred buff up to 12s duration, which basically gets you where you want to be.
The bigger question, to me, is whether that investment is worthwhile.
For DPS, I don't think it is. Keep in mind that the Battle State buffs only affect the Captain. So, your DPS will be increased by burning through your whole DPS chain and repeating it more than by sitting in Battle-Ready for a long time. I would tend to use Battle-Shout > Sure Strike > Cutting Attack > Grave Wound > PA/DB > Sure Strike > Shadow's Lament (if available) > Repeat as my DPS rotation. With animation times and the like, this basically brought me back around to Battle-Shout again by the time I was done. If Shadow's Lament is on cooldown, it might be best to fit a extra Sure Strike in somewhere before using PA/DB.
For Healing, the situation is somewhat similar. Valiant Strike granting Battle-Ready means you can usually just re-enter Battle-Hardened through normal use of your rotation pretty quickly, to the point where increasing the Battle State buff duration grants you that much extra uptime during the healing phase of your rotation. Healing Captains also feel the "loss" of empowered Rallying Cries more than the other two, who naturally get more Defeat Events anyway (LtC from crits, LoM from partial BPEs), so the legacy's effect on DE duration could indeed be useful there.
However, extending the Battle State durations could be very useful in an LoM spec, for the simple reason that LoM Captains only have one skill that starts the Battle State chain. So, the LoM strategy would indeed favour increasing the duration of the Battle States rather than simply trying to run through the chain faster. Tanking Captains are also more likely to be targeted by stuns and disarms, too, so increasing Battle State duration prevents them from "losing" skill uses that way.
In short: I'd definitely leave Battle State Durations off a DPS weapon, definitely put it on a tank weapon, and I might consider it on a healing weapon. In practice, I'll probably use two weapons. I don't think the legacies for a healing weapon are too well-defined, so most likely I'll have a DPS Weapon (no Battle State legacy) and a Tank/Healing Weapon (with Battle State Legacy).
Cainwen Ciaphas, Captain of Crickhollow, HERO OF MIDDLE EARTH!!!
I will not be pushed, filed, stamped, indexed, briefed, debriefed, or numbered! My opinions are my own!