The USB storage on my router is very unstable, as another poster said. It lets me see the drive, but a few minutes later, it's not there anymore and any file copy fails. Since your router does not even have a USB port, this option is out for you anyway.
NAS (a device connected to the network with a network cable or wireless instead of USB) is the most stable and should be faster. Or share the drive from a computer, although that requires the computer to be on all the time you want to use the drive.