In short, they would have been dead-eyed bellowing brutes. They likely stank, too. But I think that Allosaurus was by far the more interesting, and it comes down to this: the T-Rex was a vast scavenger, a chewer through corpses; the Allosaurus was a leaner and certainly meaner hunter, using a wide-jawed bite to kill.
Allosaurus had a smaller and lighter frame, made for running and it had longer arms by far. The Wikipedia entry for the animal cites detailed study of breaks in those arms showed that the creature actually used those arms. It was a capable beast that ate what it killed. By comparison, the T-Rex was a massive lumbering critter that couldn't turn quickly, may not have been able to run, and would suffer terribly if it went down badly. This wasn't even the cunning sort of food-stealer that a lion is; the T-Rex would had just stumbled along, following its nose and screaming at anything that got between it and the next corpse.
Or so it seems to me, and while I'm neither a professional scientist nor a specialist in these animals I sure have had to answer a lot of questions, causing repeat investigation (I only make up answers to important stuff; for trivial matters I research my answers. I learned this from the Tao Te Ching but I may be misinterpreting things). So I've read many sources to The Boy and shown him every educational video made on the beasts in decades. And so there you have it; T-Rex gets all the glory in the eyes of four year olds but it was if anything just a more repulsive version of the other Tyrannosaurids that went before including the relatively sexy Allosaurus.
The Boy has been able, since shortly after his third birthday, to spot the difference between the two creatures by counting their fingers. And 'carrion', incredibly, was one of the first English words he could say. Hopefully I'll be able to someday convince him that T-Rex is nasty. Enlisting scholarly videos such as that below will doubtless help my cause.
Edit, 2017: Added link about T-Rex not running. My suspicion's been confirmed.