TBH, it shouldn't. I have the same chipset in my laptop and verified the same in both Windows and Linux. Realtek stuff is pretty generic and, in my experience, performs equally well, regardless of the OS.
If you really want to check, open the property sheet for your network card in Device Manager. Click the Advanced tab and select Speed & Duplex in the property field. Click the dropdown under Value and you'll see all the options for your hardware (be sure not to change it). In my case, it matched the info given by ethtool.