I've had issues powering an external hdd on a raspberry pi or odroid. I had to buy Y-cable (Y-cable = branched USB cord for dual power).
I found out, that powering the raspberry pi or odroid on the normal USB supplies more power than on the mini/micro-USB they use. The micro/mini USB used for power has a fuse that cannot supply more than 1A, but powering via one of the USB typeA works fine. Of course you would need a Y-cable, because even the most powerful USB chargers cannot produce enough power on one port.
That's another point - most USB chargers say they produce 2A or 2.1A and the crappy ones produce .3A, the good ones go up to .9A. So everybody lies. But .9A is good enough with a Y-cable.
The PI/Odroid use like .5A, the drive uses .3A, but they spike to more than 1Amp.