In general, you want to play at the highest resolution available. Also, since you have an HDMI cable, you can play in 1080p and take advantage of improved video and audio quality. The component cables that come with your Xbox can only support up to 1080i.
The only reason why new HDTVs that can support HDMI and 1080p still support 720p and 1080i is because component cables (Some which only support 720p), are still common.
Wait so 1080p is better than 1080i ? I've been playing in 1080i for the last couple months..... i notice that on loading screens whenever the screen is all fully black i notice little inverted lines coming down my screen but i never see them in gameplay.
@Uneasyjmitchell I can tell you that I have 2 xboxes in the house, one is on a 1080i tv and one on an older one that only reaches 720. The difference is immense for spotting people hiding in bushes or shadows.