Battlemaster would have to be the most boring archetype ever. Moar damage is an awful counterbalance to versatility. It just stops a DM from being able to provide interesting combats. Also the archetype puts the fighter ~50% above the rogue in damage, and that's before we bring in the current fighter builds with GWM and polearm mastery (which already push fighters above rogues by my understanding).
My only issues were with the archetype being so much better than other fighter options that it would become another ranger- only one archetype worth taking. I'm not too worried about comparing it to other classes. The fighter SHOULD leave the rogue, and most other classes well behind in dealing consistent damage.
At the high levels it does a tremendous amount of damage, low levels you are looking at +1 damage on average for one handed martial weapons, since it's just a +1d2 increase. The extremely high levels you are rolled 3d10 for a long sword, but that's compared to a cleric with his divine increase, a rogue doing 8d6 on a sneak attack, or a wizard just nuking the board. Compared to other fighters it doesn't really compare to EK because of the magic, or the versatility of the battlemaster. The champion is kinda meh though.