The ebuild for net-misc/r8168 will abort if r8169 is enabled in the kernel configuration. This condition should be relaxed to allow r8169 to be configured as a module, in order to allow switching between the two drivers on the same kernel.
I'm probably going to close this as a dupe of bug #403021 but I'll hear you out first. I don't think it's that simple because the r8169 module will automatically load first unless you patch that behaviour out or possibly if you blacklist the module? That aside, why on earth would you want to do this anyway? If r8169 works for you then why would you want the added headache of an external module? You should only use r8168 if r8169 doesn't support your hardware revision. Note that the number of revisions it supports has increased over the years, my hardware didn't work at first but now it does.
Oh well. *** This bug has been marked as a duplicate of bug 403021 ***