I don't know the technically exact cost but larger textures should not incur a significantly larger cost to switch to or from - if any at all - than a smaller texture.
It's the switching that's costly but why it's costly and how costly it may be may or may not be partly related to its size.
The 'solution' to your question is a third option, re-order so that all the draws with the big texture are drawn next to each other (or even as one) and the small texture together the same way.
If they 'must' be drawn in this way, consider adding the small texture to the big texture.
With the 'alternating small textures', you could always combine them both into one, reducing the switching of textures and potentially reducing all of those alternating draw calls to just one.
Just remember, if you're trying to be efficient with your textures, use one at a time (avoiding switching) and draw multiple objects using that texture at once (avoiding excessing draw calls).
So, to provide a possible solution to your original post:
place the textures for both sprites into one image (you can do this programmatically if you'd like), and then load it to a texture. Then, draw each sprite with that same texture but use the texture rectangle (textureRect) to specify which part.