I guess it depends on whether you care about whether the rivalry is one of skill, or just naming rights. Yes, the Apple Cup and the Civil War are things in their respective home states, but the series isn't especially competitive. Conversely, you could argue that Oregon hasn't been especially competitive with Washington (although closer than Oregon State is to Oregon). Washington hasn't been that competitive with USC, either, but not many schools have been (and ND has about the same edge over USC as USC has over Washington).
I think beating each other is more important than beating their in-state "State" brethren, but mostly because Washington and Oregon fans expect to do the latter. Or maybe it's recency bias and the fact that without the Pac-10/12, those games don't exist anymore. Which is sad.