Which is better 720p or 1080i? I have LG LCD tv and native resolution in 1360x768. I noticed that in 1080i my screen is better centered. Both modes looks same to me.

Your TV has a built-in scaler. Just use what looks best to you.

1080i has more lines. But 720p refreshes the picture more. I prefer 1080i

Topic is offtopic, and so it is reported.

There is nothing 'better'. Both modes have their advantages/disadvantages, just like with PAL and NTSC.

Technically, for your situation (your TV, plus the fact that you play games) 720p (1280x720 progressive) would be better than 1080i (1920x1080 interlaced). It's closer to the native resolution so less scaling is needed, plus it's progressive which will give a smoother image when there is a lot of movement.