I had a C6300, little older model than the one you're looking at, however both are from the series 6, and those are very well known for rotten awful input lag, even in game mode. Mine lagged behind CRT(standard definition) by about 50ms, which is just horrible for gaming. It's not easy to see, but you can feel it in the controller. Aside from that though, it was great. No ghosting or banding whatsoever, very good for cable and movies.
The only way to be sure is either to scour the internet for speed tests on your particular model, or take your 360 to the local Best Buy and kindly request that they allow you try it on one of their display sets. You should be able to tell if it bothers you or not. Especially if you try it with a shooting or racing game, you will be bumping into walls, misfiring and swirving all over the place if there is significant lag. These numbers are never printed by the manufacturer, they'll tell you the response time, but never any input lag figures. It's up to we, the consumers, to discover them.
I have the Samsung LN46D630 and it's worked out great for me. With game-mode on, I haven't noticed much input-lag at all, and I can play games that require precision button pressing. On another note, with game mode on, the picture looks a bit more rough and brighter. I wish the 120hz optionwould work in gaming mode, but the lag is just too much. It instantly makes any game look like 60fps, but the lag input is horrible.
Ah interesting. I've seen mention of people turning off all processing options, is that what you did, or do you still have some running? --- "Life is a mistake that only art can correct" - from Passing Strange
I didn't really experiment with those settings at all. One thing I've heard a lot of people say about this particular TV, however, is that if you plug the HDMI into the "PC" option, the input lag is supposed to be lessened a bit. I remember doing this when I first got the television, and it's been on that option ever since.
Game mode essentially turns off all pre-processing functions. You'll also want to use nothing other than hdmi or vga. The latter works a little bit better if you're looking to minimize input lag as much as possible, but it does have the side effect of washed out colors and a less crisp picture. I'll say right now if you want the best gaming experience possible (meaning ordinary television is a non-issue), a good monitor is what you want. They're much cheaper and much better for gaming.