I never noticed any performance difference between the two modes myself. The 2 main advantages of AHCI over IDE though are hot swap and NCQ (if the drive supports NCQ).
Hot swap means you can replace the drive or unplug the device from the computer without rebooting. NCQ (Native Command Queuing) allows drives to accept more than one command at a time and dynamically reorder them for maximum read write efficiency. But NCQ is only a benefit if you are running very intensive disk operations which may not be the case for the average home user.
Practically speaking, use AHCI if your hardware supports it, as it can only enable features of your drive to be accessed. It should be the same or faster than IDE, unless you have a very bad sata controller chipset or something. Also I think some of the first SATA drives supporting some features like NCQ actually did better with them disabled, but I think that is no longer the case.
Yoy can also go through this thread.
Change IDE to AHCI in BIOS - Much better performance