Vow of enmity only give you advantage though... haste and misty step are just mobility. Hitting enemies aren't that hard in general, and movement isn't actually that important in combat, unless you are multiclassing as a hit and run rogue or something like that.

For fighter subclasses, which is better for combat:

Battle master, or psi warrior?

Battle master dice start out better for damage, but psi warrior has intelligence bonus, so is actually better. Also, the psi warrior ends up with more d12s. The use is also more versatile for psi warrior. The only real thing that seems better about battle master is the effects of the manoeuvres. 

Needing Intelligence is actually worse. As a Fighter, you'll want either Str or Dex and then Con. Battle master works with this. Psi Warrior then makes you invest in Int, a third (or fourth, depending) Ability Score, making it harder to max out and therefore hit your potential.

Fair. I guess you get less hit points. And relentless is pretty good in long fights.