There are many reasons to make the decision between an HDMI cable and a component cable for your Xbox 360. These include cost, hardware (meaning TV) and level of gaming in which you partake
While HDMI cables can be obtained for around $30, to ensure the best performance it’s best to go with the ones that cost $100 or more. Component cables are essentially free, given that the system comes with them. Each can be purchased for $40 from Xbox.com.
The Xbox 360 renders its graphics digitally. A component cable transfers data in analog format—meaning the data is created, compressed and then expanded. The result is less clear edges and images. HDMI cables transfer images in a digital format.
Usually only plasma, LCD and LED TVs contain an HDMI port. Even then, it is not guaranteed. Unless your TV can render 1080p graphics, it might not have an HDMI port. Meaning only component cables will work.
HDMI cables, because they never compress data, render much better and cleaner images. Component images are rough on the edges.
Unless the best graphics are important to you, stay with a component setup. Neither HDMI cables nor component cables will affect game play.