This is an interesting question, and one that I probably can't answer with much accuracy due to my rather superficial understanding of entomology. I'll give it a try though from what I observed while owning these specimens.

First a defensive: My emperor scorpion had a thin but durable exoskeleton, with the segments on the thorax being thinner than the coverings around the claws and legs. My tarantula had an exoskeleton of comparable thickness over it's entire body while also having a dense mat of wiry hairs covering every bit of the exoskeleton. These hairs irritate exposed flesh and would deter a mammal, bird or reptile but would have little to no effect on the scorpion. For maneuverability, the emperor scorpion had greater lateral movement speed than the tarantula, but less horizontal maneuverability. Both species could tuck in their legs to their sides but neither had any way of covering the top of their thorax. The face is somewhat of a vulnerable area for both creatures. The emperor scorpion has two large claws to cover its face and can still attack with its primary weapon, the stinger, while doing so. The tarantula can cover its face with a wall of front legs but loses the use of its primary weapon, the fangs.

Now offensively: My emperor scorpion has two claws capable of restraining the tarantula, but incapable of piercing the exoskeleton. The curved stinger on its back would easily pierce the carapace of the tarantula and would also inject it with a sizable dose of imperatoxin. The actual piercing may damage internal organs or disable the use of an eye, but I am uncertain what the effects of imperatoxin has on a tarantula. Imperatoxin is deadly to small mammals, reptiles and other invertibrates of comparable size so I will assume that the toxin will have an effect on a tarantula. In addition, the tail moves like lightening when the scorpion is determined so it can sting over and over again very rapidly while depositing venom. Like I said, this is merely speculation on my part as I have little knowledge relevant to your question outside of what I learned caring for them. Perhaps /r/askscience might provide a more informed answer. The tarantula on the other hand has greater leg strength (from what I observed while watching him roll things about in his aquarium) and two fangs that are significantly larger than the scorpion's stinger. However, the tarantula I had did not have any venom glands, so a bite would cause physical trauma to the effected area but would not poison the scorpion. In addition, my scorpion came up to my tarantula so they will be fighting in his habitat, in which he has a slight advantage over the scorpion by being able to get above the scorpion.

The verdict: The tarantula would most likely latch onto the top of the scorpion's thorax since that is the largest and first available target. The scorpion would then grab onto the legs of the tarantula and sting the first thing it can reach, most likely the top of the tarantula. The tarantula would thrash about trying to pull free while enduring sting after sting. Eventually the imperatoxin does its work and the tarantula dies.

Although this is a somewhat unlikely scenario since neither of these creatures would find the other to be worthwhile prey being very similar in size. More than likely these two would meet make their "I'm a badass!" pose and scurry away.

tl;dr I think that the scorpion would win due to having his venom glands while my tarantula's glads were removed. But really, I'm talking out of my ass here.