The wheels on the LTZ don't have the gaps that the LT2 has. There's a lot of space between each spoke on the LT2, so the brake dust can easily get on the inner part of the chrome. Also, it's more noticeable on chrome wheels, because they're shiny. Even a little brake dust dulls the finish.
I had wire wheels on one of my cars. They made a special spray for them that contained a mild acid. They came out sparkling clean and shiny with no effort at all. You simply saturated the wire wheel with the spray, let it sit for about a minute, and hosed it off.
I wonder if they make a similar product for chrome wheels.