Ummm, no. I said Improved Initiative is not important when both side's got it. Initiative is important, but only for the first round. After the first round, somebody is always going before someone else, so how is Initative SOOO important then?
Waitaminiute. Are we still talking about Rogues, here? Cause if we are, then the rogue's gonna have a goddawful Dex, and even with Improved Initiative you ain't gonna beat his Init. He doesn't have, and you get, then possibly you could beat the rogue. But, only if you give up the high DCs to spells by pumping your Dex, just like he did.
You seem to get it, but still drift into somewhere else now and then. Initiative measn something, at all levels, in fact, but only at the start of combat. Improved Initiative is only going to get you anywhere at low levels, unless you're in a class that pumps up Dex as routine. Even then, it becomes inconsequential at high levels.