Capture of Black Ops 2 on the Xbox 360 using a $70 capture card from eBay. Search eBay for "HDMI Game Capture Card USB 3.0 1080P 60FPS Game Live Streaming Recorder Device" to find the exact model.

I used OBS to record with NVENC encoding. The video quality is fair but appears to have a slightly sharp image. Almost like the soft edges have been removed. This may be fine for most people but it is noticable when compared to the actual video output from the Xbox.

I had to adjust the audio offset by 350ms in OBS to get the audio in-sync.