Different computers are going to be able to pull data at different speeds through USB 2.0 sometimes just depending upon the hardware and operating system alone. Even still, 6 MB/s is pretty slow transfer speed but not too absurd on 100 megabit connection. The theoretical maximum of a 100 megabit connection is only 12 MB/s, so given that there will be some loss due to connection latency, distance, and the amount of time it takes for the source computer to move read data through the USB 2.0 port from the external hard drive, to memory, to the NIC, across the network, through whatever network devices you might have til it reaches the end device.
Does your network run through a basic switch or a router of some sort? It's possible you are experiencing a slowdown at the router itself as packets are inspected and sent on. Most good switches or routers will not impact the switching speed or switching capacity much, but cheap ones will not be able to even offer the full switching speed that they are rated for (such as 10/100 or gigabit.)