Elgato is the best capture card out there in the market. It's cheaper than some of the options out there, very small (My iPhone 5 is longer than the thing though it's about half a centimeter wider and 3 times as thick, which is still pretty dang small), easy to set up (How to set up: Plug in HDMI from Xbox to 'HDMI in'. Plug in HDMI to TV from 'HDMI out'. Plug USB cable into computer USB port. Complete.) and comes with a fairly decent software for capturing (Elgato Game Capture HD, which has some VERY unique features that exist NOWHERE else in the market that is best used for capturing live gameplay [flashback recording]) and the videos are captured in high quality, easily edited formats, and you can also upload straight to youtube from the captured video on the software. Further, it also makes it possible to stream gameplay to both youtube and twitch.
Elgato is legitamitely the best thing out there, and they've partnered with like a billion gaming YT channels that give users a discount.