While IMAP IDLE provides real-time notifications to your client, it differs from ActiveSync in many ways. IMAP IDLE is an extension of the IMAP protocol (as described here) and IMAP being a message protocol, it handles only email. ActiveSync (as described here) handles email, calendar, contacts, notes and tasks, and syncs them across all of your clients (that support ActiveSync, including devices).
ActiveSync for example, if you added a new contact on your phone, your desktop client would instantly also have the contact available. The same goes the other way too, if you create a new calendar event on your desktop client, your phone would instantly have the event as well.
IMAP IDLE can also only generally receive notifications for the folder you currently have selected / viewing. ActiveSync does not have this limitation and receives real-time notifications for all folders.