Why does the color of this hillside rock vary?
It's pretty hard to say anything about this kind of weathering without actually being there and having a closer look.

Usually, the simplest explanation for reddish or brownish colours in otherwise grey rocks is the presence of iron oxides. You can see that the brown area is on a fault or joint face. This leads me to think that maybe this was a conduit for groundwater that oxidised the rock. When the road cut (or whatever it is) was made, this part was exposed. Notice that you have some brown elsewhere - it could be that those are faults or joints cut perpendicular to the face, so that's why you only see a brown streak instead of a surface.