Does a 2.3X:1 movie need less bitrate than a 1.78:1 movie?

[MisterFantastic]

Simple question that I've been wondering, does a movie that's matted with black bars (ie a 4:3 movie, or a 2.35:1 movie) need a substantial amount less bitrate than say a transfer of the same content, but at 1.78:1 (fullscreen)? The reasoning behind this would be that since the black bar mattes are always constant, the codec would need less space than something that fills the full 1920x1080 frame with information.
Would the difference in necessary bitrate be negligible, or would substantial?