OK, Asteria might have a self-defense beam pistol, or dagger, but would otherwise be purely support.  Asteria might also have a riot shield.  Healing was a function that I hadn't even considered, so I'm glad you thought of it, it's definitely a unique ability that would make the Asteria extremely valuable.  Maybe in the future, the Asteria gets more armor, but then the armor pieces are these self-propelled, remote controlled shards that can be sent out to increase the armor of an ally.

Nyx would probably have some sort of melee weapon (choose your favorite), maybe she can dual-wield, with one being a beam weapon, the other being a mass weapon so she can break through any type of defense.  Do you want to push the 'ninja-like' aspect for Nyx?  Maybe in the future, it can develop cloaking or afterimages as a suggestion.

As for their combination, the most simple suggestion would be that they combine to become a larger cog.  It would probably be fairly well rounded defense-wise, having armor from Asteria and speed from Nyx.  Maybe Nyx's melee weapons combine to become a large one-handed melee superweapon, while wielding Asteria's shield in the other hand, or the shield also becomes part of the superweapon.  Maybe the combination has accelerated self-repair from Asteria.  Again, these are just suggestions.