A USB Thumb drive is nowhere near the speed of a USB3 HD.
With a USB3 HD (connected to an Intel USB3 controller), you should see the full speed of the HD.
ie: If the HD would sustain 150MB/Sec connected via SATA-III, you should see 150MB/Sec connected via USB3.
USB3 tops out ~550MB/Sec sustained.
FWIW, "e-SATA" stands for external SATA.
Internal SATA drives are just referred to as SATA HDs.
e-SATA (external SATA) is typically limited to SATA-II (which really isn't much of a limitation with conventional HDs).
That being the case, USB3 would have more bandwidth.
With that said, USB enclosures often have firmware that (automatically - with no ability to change) put the HD into sleep mode after a brief period of inactivity. This is a royal PITA if used for anything but backup/transfer purposes.
Intel SATA-III controllers (internal SATA ports) offer the most bandwidth.
Think of Flash Drives as a means of portable transfer.
That's their designed purpose...
They offer nowhere near the speed of a fast conventional HD and certainly nowhere near the speed of a fast SSD.
A fast 2.5" SSD sustains ~520MB/Sec when connected to an Intel SATA-III controller.
When connecting to 3rd-party SATA-III controllers, this figure typically drops to ~360MB/Sec sustained.
In short, just make sure the bus you choose isn't limiting performance.
A conventional SATA HD will perform about the same (MB/Sec sustained) when connected via: Intel SATA-II, Intel SATA-III, e-SATA, and Intel USB3.