rozroz, eSATA is definitely faster than USB2, no doubt about that, faster than FireWire as well. However, when it comes to specific devices, things may or may not be properly implemented.
For example, I have an old Seagate external hard drive. When I connect it to my laptop's built-in eSATA port, the speeds are well into 100 MB/s (as reported by Windows). Now, my desktop does not have a built-in eSATA port, instead I have a PCI-e add-on card. Here I have some problems with drive recognition and the speeds vary between 20 and 50. On the other hand, USB2 is hardly ever faster than 20.
Recently, I was looking for a new external hard drive for myself and I would not buy a drive without eSATA connection. However, given the appearance of USB3, eSATA drives are relatively rare. I am starting to think that an eSATA enclosure, for example such as TCG was talking about, is the way to go. After all, any external hard drive is just a regular hard drive already packaged into a nice enclosure (personally I never use the software that comes with those drives).
Finally, for your specific issue, I am not sure what's causing it. If you bought the drive recently, I would definitely exchange it. If, however, the problem persists, I would examine your system (
drivers, etc.) as I doubt you'd be so unlucky as to get more than one defective drive in a row.
Edit:
What you're reporting as a slow speed comes up to roughly 1.9 MB/s. I've seen speeds like that with USB2. Try to check what your antivirus is doing during these transfers. Also, sometimes it's just Windows, maybe someone else will know more about what Windows is doing during the file copy process, but to be honest, I am rather unhappy with how copy is implemented in Windows 7.