After some consideration, I think I have a plan for what I want the three factions of "Hexgame" to be. Each of the 3 factions corresponds to one of the 3 genres of speculative fiction = Fantasy, Science Fiction, and Horror.
Fantasy: The Paladins
Medieval-era human beings with mages and magical beasts to back them up. They'll have a balance between cheap non-magical units and more expensive, but quite powerful magical units, and will favor a fairly balanced and standard gameplay style.
Science Fiction: The Cogs
A faction composed entirely of steampunk automatons. This race's units are powerful and expensive, favoring a player who can turtle for long enough to build an overwhelming advantage.
Horror: The Bogeys
A faction composed of horrific monsters. The Paladins call them demons, the Cogs call them aliens, and everyone calls them scary. Their units are cheap and very powerful in the right situation, terrorizing the unprepared enemy, but weak when countered correctly. They favor the player who can surprise their opponent and take them down before they're ready.
In addition to the normal single-target units that make up each race, each race will have one or more "hordebuster" units that deals damage to multiple units at once. How those units work will be unique to each race.
The Paladins will have a unit with a magical death ray which can be fired out along one of the hexagonal grid's 6 cardinal directions, damaging all units in a line (out to a certain range). Think of them as cannons, they support your primary force and soften up the enemy for your other units to take out.
The Cogs will have a long-range catapult that launches exploding projectiles, dealing splash damage to all enemies within a 1 hex radius around its target. Allow a Cog player to build up a force with several of these and enough protection to keep them alive, and they'll decimate any foe with a hail of destruction.
The Bogeys too will have a unit with an explosive attack, but instead of a ranged projectile, it will be a unit that damages all nearby enemies in melee range. I'm thinking of making it a suicide unit. In any case, it's designed to allow the Bogeys to overrun your defenses and demolish your stuff.
That's what I have planned so far, let me know what you think.