T rex was adapted with a strong bite to hold prey that was smaller than himself, shake it and crush it. The biggest Triceratops is still smaller than a T rex. Hadrosaurs are slightly smaller but compareable. Allosaurus was build to hunt Sauropoda. Animals a few dozens time bigger than himself. Thats the main reason why Allosaurus has a weak bite but sharp teeth. It would not make sense for him to bite into his victims. He hacked with his upper jaws into it to cause wounds and bloodloss. Different strategy of hunting and different prey items. And any hadrosaur or triceratops is small compared to the sauropods.
I never intended to compare a late Cretaceous coelurosaur to a middle Jurassic allosaur; that is an apples and oranges comparison. hatchet bites vs crushing bites are well established with how effective they were. They were both deadly effective, but they were intended to kill different organisms. Theropods with a hatchet bite were, as you said, specialized predators that targeted the large, lumbering, nearly immobile sauropods. Their modus operandi was quite simple. Run in as a pack, gouge out a bunch of chunks of meat, run off, repeat as necessary, and wait for your prey to bleed out.
However, rex was sympatric with animals like Edmontosaurus which was as long as rex and just as massive. To say his prey was 'smaller' is to misrepresent what was likely happening in their world. Rex specimens such as Sue were often larger than most of the orinthopods with which they lived, but your average rex wasn't as big as Sue, either.
Regardless, its apples to oranges. I suspect the reason that rex evolved the hyper powerful jaws that it had was in order to take advantage of a resource from its kills that wasn't being utilized by any other animal in its ecosystem: bone marrow. The carcharodontosaurs, the direct descendents of the allosaurs, had to deal with 'cruncher crocs' such as Baurusuchus, who are thought to be akin to hyenas in their behavior. Rex, not having competition for this resource, adapted to take advantage of it. Of course on top of all that, there were no sauropods in late Cretaceous North America.
Now, here's a question that I'd like to hear some people's input on: At parity (40 ft long, 7 tons) who would win? A hatchet bite Giganotosaurus or a crushing bite Tyrannosaurus rex?