Dang, Trashed those are both 2.5" form factor drives. I couldn't find the RPM speed so I don't know if they're 5400 or 7200 RPM but I'd guess the slower. The USB 2.0 spec calls for a .5ma output if I remember correctly. If it's not delivering enough power through the USB port it's possible you're right and it's basically "starving" the device. I'd be interested to see how it would work with my 3.5" custom external enclosuers that use external power supplies.
If it's just a matter of power delivery then something like
this DC powered USB hub might fix the issue.