It would depend on which Josh showed up.
If it was a Josh that wanted to sub, Josh would take a UD. Both guys are good enough on the ground to avoid being subbed by the other and Josh would take it with top control and take downs.
If Josh wanted to GnP, he would probably stop Mir in the second or third.
However that's just my guess. Since Brock pounded Frank out from the half guard Frank seems to have really changed his game on the mat, from what I've seen in seminars and videos of his. And we haven't seen him on his back yet since UFC 100.
Think. It Ain't Illegal Yet
"Discipline Hurts Less Than Regret"