Performance wise, it makes no difference - on standard commodity chipsets, there's only one PCI bus, so onboard chips connect to the same PCI bus as cards do.
Drawbacks of Onboard are (1) when you upgrade mainboard, you can't keep your controller, and (2) you can't use BIOS updates from the controller maker straight away, you need to wait for the mainboard maker to include a newer controller BIOS into the main system BIOS.
The former is about money and possibly having to reinstall your OS after the update (in case you can't buy the exact same controller anymore, which, in case of IDE is quite likely) ... and the latter proves to be a major annoyance especially with IDE controllers, the rate at which BIOS updates for those appear is still quite amazing.