Better to use multiple objects or textures with basic paperdolling?

I'm designing a game for iOS and android.

For a while I've been using some tacky stand in for my texture, but now I've designed nice looking textures.

My game uses colours to demonstrate which player is which. Previously I was just differentiating between colour to show which player it was. My "characters" are 2d sprites.

Now, my problem is, only the main body of the character should change, not its detailed features.

I can have hundreds of these things moving on screen at any time so I need the most efficient method.

Would it be better to just make a bunch of textures that have different colours, or 2 Gameobjects per character, in which one contained a transparent cutout overlay of all the detail, and the one underneath which has the outline with a white inside, whose colour is changed instead?