The focus of the warlord should be on Intelligence first and foremost, with flavour suggesting tactics and strategy and general knowledge of warfare and enemy actions.
The Charisma-based warlord is fine, but overlaps a little with the bard. Having both classes inspire through rousing charismatic speeches is an unnecessary overlap. There could be some inspiring warlord design later, but it might shouldn't be a core build unless there's some free space.
I think some freedom in weapons would help differentiate warlords. By not mandating Strength or Dexterity, warlords could stack one or the other and favour heavy weapons, ranged weapons, sword & board, etc. Warlord powers could be ranged neutral just mentioning spending an action to attack or attacking with a weapon.
Martial Damage Dice and maneuvers would really compliment the warlord. As they get more MDD they can help more allies at once, eventually moving or buffing the whole party, or really stack a boost on one character.
Unlike the fighter, who is differentiated by their weapon choice, the warlord should not. That's a big difference between the warlord and fighter, none of their builds or choices should depend on weapon.
I think you can break the warlord down into a few different builds: offensive, defensive, and debuffing. I think all builds should have some movement component; all warlords should have the ability to reposition allies, spending a MDD to move an ally 5 feet. That's their "parry" that all warlords get.
An offensive warlord would focus on giving his MDD to allies, granting extra attacks, negating attack penalties, and potentially granting advantage. Defensive warlords would reduce damage against allies, grant DR, mitigate crits, grant saves, and the like. Normally I'd include spending Hit Dice in combat to heal here, but today's
Legends & Lore article suggests might not fit their simple core. Debuffing is something warlords haven't done a lot of in the past because they were trapped in the "leader" role and debuffing is part of a controller's job. But you can certainly turn the warlord's powers around and use them on enemies, stopping or inducing movement, imposing penalties to attack or damage, preventing reactions, etc.
A different direction would be to rework the warlord. D&D has a history of a "cavalier" class, the mounted knightly warrior. It's always been a little awkward because it overlaps with mounted fighters and paladins. The warlord shares a lot of similarities with a leader-build fighter. Combining the two classes gives them both extra flavour and more differentiation from the fighter.
In addition to the other builds above there might also be a "mount" option, where the class inspires their steed so the two fight as one.