In the case of Nikon cameras, you can at least precisely match the colours of the in-camera Jpeg:
http://rawpedia.rawtherapee.com/How_to_get_Nikon_ICM_profiles_from_NX2
The demosaicing, noise reduction and lens corrections will still be different, but you processed RAW will look very close to the Jpeg produced by the camera.
I can give you detailed instructions if you are interested, personally I use this method almost all the time to have a good starting point for my edits. One can always go back to the default Adobe camera matrices if a more neutral result is needed…