Ngl I use both often so I may be biased.
The Broken War is one of the best single-sword weapons in the entire game.
-good damage
-great crit chance
-slightly better than avg crit. multiplier
-decent status
-normal attack speed
It's such a solid weapon to have and use.
Plus, you have four different stance options to use on it.
I can't recommend the Broken War enough.
War is kind of a different story.
-very high damage
-but hits slow
-good crit
-good crit multi
-good status but don't forget it swings slow
-B I G range
Even though it's Impact damage, damage is still damage. It still hits very hard,
It's got great range but hits slow.
I'd honestly say it's outclassed by the Paracesis you get through the story.
That being said though, I still highly recommend the War.
It's my most used melee weapon to date, despite owning a Galatine Prime which is pretty much better in every way to War. I still use War in my general loadouts.
I also just use it a lot because it's just too damn cool to look at. And that it's very ironic to kill Stalker with it.
(Plus, the Tempo Royale stance is just too damn fun)
TLDR
Broken War p good
War is good but outclassed, get for fashion