The ICQ application is exactly the same as AIM except for its green theme. The only thing is that ICQ is free and doesn't have any ads. You can still log in with your AIM screenname, as it is all the same network now.
You can indeed use the ICQ for iPhone client to log into the AIM network with your AIM (or .mac/MobileMe) screen name, but the ICQ client doesn't have the benefit of multiple screen name support, long lived signon and SMS notification of received messages (for users in the US, Canada and other locations where we offer SMS services) or Contact List support, among other more minor features.