Switching to HDMI will not fix input lag. Lag on Xbox 360 (especially original Arcade/White models) comes from:
Component (YPbPr) supports 1080p on 360. If your TV has a low-latency component input (rare), it can beat a high-latency HDMI input. Test both with a lag tester (Leo Bodnar) or Rock Band calibration.
Bottom Line: HDMI = better picture, not lower lag. Fix the TV settings first.