Does the oxygen concentration equilibrate between red blood cells in the liver sinusoids?
The oxygen saturation (in lungs) and desaturation (in target organs) takes place via diffusion along the concentration gradient (i.e. partial pressure for gases). Therefore as long as RBCs from two different sources and having different partial pressure of oxygen mix up, the oxygen level starts to equilibrate between these cells.

But diffusion as a passive mechanism is not very fast and can take some time. So the only possibility for the second variant (there is a mixture of two types of RBCs) is if the mixture exists for very short time in liver sinusoids, so that the blood leaves them without really mixing completely up.

This is not true, at least in some animal models the blood within the liver seems to reach equilibrium very quickly and its resulting partial pressure can be influenced by adjusting the blood flow from different sources (using vasoactive substances injected directly, as in the referenced paper).