By the way, a quick remark: under iOS7, the video bitrate setting only has effect in the default (iPhone4: 720p; all other non-iPad2/iPt4G devices: 1080p) mode, not the full-sensor oversampled one. In the latter, the default bitrate is used and AVCaptureDevices[0] > AVCaptureSessionPreset1920x1080 > VideoCompressionProperties> AverageBitRate is fully ignored.
I don't know the cause for this. Under previous versions, the oversampled mode didn't ignore the bitrate setting. (I've shot a LOT of oversampled videos back in the 6.1.2 days at much lower datarates on my iPhone 5 so I know this was indeed the case back then.)
I've tested this under both 7.0.4 (iPhone 5) and 7.1b3 (iPad 3).
All in all, under iOS7 (only), if you use oversampling (the wide mode), no matter what value you set on the right picker, it will be ignored and the default data rate will be used. Which is a bit of a bad news...
On the other hand, if you stick with 1080p (on the iPhone 4, 720p) mode and don't use oversampling, the bitrate setting will work OK. This, naturally, also applies to the iPad2 and the iPt4G receiving support in the latest beta and entirely lacking the default resolution vs. oversampling picker.)