No. The external storage speed issue is related to the connection type (ie: USB) and not the disk speed. And those speeds are slow if you have a USB3 external drive and are using an actual USB3 port on the PC.
For reference, I can copy 400GB to a drive in about 2 hours. This is a bare drive in a eSATA dock and is only writing at 40-50k (should be much higher and I am currently investigating that issue). I also have a new external Seagate 8TB USB3 drive that I am using for testing, and the speed writing to that drive is 180-220k (so 4 times faster, which would equate to only a 1/4 of the time to transfer 400GB).
So your issue doesn't appear drive related, it's USB port related. My guess is you are using a standard USB (2) port.
For reference, I can copy 400GB to a drive in about 2 hours. This is a bare drive in a eSATA dock and is only writing at 40-50k (should be much higher and I am currently investigating that issue). I also have a new external Seagate 8TB USB3 drive that I am using for testing, and the speed writing to that drive is 180-220k (so 4 times faster, which would equate to only a 1/4 of the time to transfer 400GB).
So your issue doesn't appear drive related, it's USB port related. My guess is you are using a standard USB (2) port.