If I was designing the system, it would be predicated on the consequences of the most critical type of error. Obviously whoever uses the outer, has to cross the inner, and the error we're looking at is a runway incursion.
If the lander crosses while an A/C taking off is in a "line up and wait," there's less pressure on ATC since they are free to wait as long as they need to, before issuing the takeoff clearance. That puts less pressure on the situation since there's no time limit for the crossing plane to finish. If the crossing plane accidentally turns onto the runway instead of crossing (or simply gets stuck), the other plane on the runway is just sitting.
If, instead, the takeoff plane is crossing in front of a lander, there's a time limit forced by the approaching lander. So if the crossing plane stays on the runway too long, that forces a goaround which opens up the potential for the lander missing the goaround instruction, or starting it too late, etc.
So both of these reasons point to taking off on the inner and landing on the outer. I think every airport I've been to in the Eastern US does this, except Philadelphia.