For additional storage, one method is just as easy as the other.
But direct connection within a system will be faster data transfer and slightly less of a hassle (since you don't have to consider whether the external drive is connected or not).
The key thing is to make sure that you have an empty IDE/SATA slot (or an empty place on an existing IDE cable) to connect the drive to the motherboard...and that you have a power supply that has leads capable of attaching to the drive.
There's probably some other consideration but that's all I can think of
FWIW: Your IDE/ATAPI controllers are for any PATA/IDE hard drives and CD/DVD devices which are connected to the motherboard.