The slowness is due to the use of wrong kernel module (detected by the OS) for RTL8169. To verify, issue a command:
We should be able to see a line starting with
Alternatively, another command could be used to generate the hardware profile of your machine:
sudo lshw -html > somefile.html
In that case, the resolution is simple. Go to Realtek download site to get the appropriate Linux driver. Expand it and follow the README inside.
After reloading the driver, use
lsmod to verify if there is a line starting with