As I’ve said elsewhere, raw bitrate means exactly the same between them, because the bitrate is the number of bits per second of video after compression. What you mean is that you set a target bitrate and the different codecs have varying success in meeting that target. You can use two-pass encoding to improve the codec’s accuracy.
But what matters is the average bitrate required by each codec to achieve the desired level of video quality, as perceived by you. The lower bitrate you need for the quality you want, the better the codec is.