Here's how I think it might go:
If IB Traveler tried to teleport, CO Traveler could just freeze time with his box and kill or speed-age IB Traveler that way.
But if IB Traveler got the box, he could freeze time, although since CO Traveler is immune to the time freeze, nothing would really change.
So I think the Creeped Out Traveler probably has a better chance of winning.