Question concerning installation of Kali to an External (USB) Hard Drive

I intend to install the new Kali Linux 2.0 release. I have a 500 GB Toshiba External Hard Drive connectable through USB 3.0 w/ back-compatability to USB 2.0; I want to install Kali on this drive.

My question is this: Should I install Kali Linux to the External Hard Drive as a Live USB Device, or should I install it to a USB and THEN install it to the External Hard Drive, the same as you would an internal, fixed disk?

I know theoretically both are possible; however, one may have more compatibility problems than the other or require extra work.

Any insight is appreciated. Thank you.