Realtek provides the source code for the r8168 driver which is based on the r8169 driver from the kernel tree if I may believe their source:
/*
* This driver is modified from r8169.c in Linux kernel 2.6.18
*/
Both are GPL licensed, so source code may be exchanged with no legal issues. That's why I find it rather strange that Realtek maintains a separate driver with no changelogs or documentation.
What's the difference for the end user? Which driver is recommended?