Tyrannosaurus rex, long held to be and for a good long while the actual holder of the title "World's Largest Carnivorous Dinosaur," (we are going to ignore the Spinosaurus completely as a tall fat fisherman amongst big game hunters for this conversation, though that is clearly a bad over generalization) was bound to be outsized by a southern hemisphere dinosaur some day. Large sauropods were the deal of the day the world over during the Jurassic and the smaller predators that took them down as food items showed evidence of conducting their hunts in packs, thus making size an important, but not a determining, factor in who eats whom and what is permanently off the menu. Pack hunting allows for smaller individuals to take down larger, as well as faster, prey items. Consider Tyrannosaurus and the slightly larger Mapusaurus as pack hunters a moment. The Tyrannosaur pack has dangerous and large prey to take down in Cretaceous North America, but their prey, despite being large and well armed, is not as large as the animals being taken down in Patagonia by the Mapusaur pack. The little bit of extra size, and potentially muscle and body weight, makes sense in the south for a totally different reason than it makes sense in the north. If your prey is larger than the largest prey of another predator then it makes sense that one route of adaptation may be for your species to get larger; remember that there could be any number of evolutionary routes Mapusaurus could have taken aside from being a large predator to take down even Argentinosaurs. Deinonychus is only one example of another route of small versus large. Instead, for many different reasons, Mapusaurus grew from chick to adult to be the largest terrestrial carnivore, albeit by mere centimeters in some individuals perhaps, of the Cretaceous.
Would a Tyrannosaurus be able to take down an Argentinosaurus, as a pack or individual, in the same manner that Mapusaurus could? The answer, of course, is not at all. A Tyrannosaur's main weapon, despite any hunter/scavenger debating, is most definitely its mouth full of teeth. The hands of Tyrannosaurs were basically a non-issue when discussing hunting tactics. They had a purpose of course, but most likely not a large role in hunting. Could a Tyrannosaur take a big chunk out of an Argentinosaurus? Certainly! Mapusaurus could use its teeth as well, though it had a narrower and longer skull, think wolf, than the bulldog-like skull of a Tyrannosaurus, if we are still talking about dogs. In fact, with the more agile hands of Mapusaurus that may be the exact way to think of Mapusaurus' hunting tactics: it may have hunted in a pack in a very similar manner to wolves to take down larger prey like Argentinosaurus. The more agile hands could grasp prey items for a momentary well placed bite or rake them with the claws and wear them down to exhaustion. Different hunting styles for different prey items, but both genera had bulk to deal with the massive injuries that could be inflicted by prey, in part at least, and both, regardless of which was actually largest on average, were enormous carnivorous dinosaurs.