When can we expect a material to look about the same no matter the rendering engine? As it stands right now, the colors resulting from the material are substantially different. Or is it off the plans?
They are trying to achieve that as much as possible.
But if the result is exactly the same, there is no reason to keep two engines instead of one.
If material colors are not the same, it is supposed to be subtle and related to lighting that is not the same using different techniques.
If material colors are very far between engines ; that may be a bug with color management or a bug of one renderer or both. In that case, devs will try to fix it.
Both engines are different in nature, so results will be different. Devs are trying to make both the most compatible possible, but they will not be the same. (Cycles is a physically based raytracer as accurate as it can be, EEVEE is not a raytracer at all, but a rasterizer that uses game engine principles to achieve speed, sacrificing accuracy).