Spinosaurus vs. T. rex

In the movie Jurassic Park III, the Spinosaurus is the biggest and baddest dinosaur yet, a worse villain even than Tyrannosaurus rex. Could Spinosaurus in fact defeat T. Rex? Spinosaurus was probably a bit longer than T. rex, though it was more lightly built. But Spinosaurus lived 10-30 million years before T. rex tromped the Earth. Had they been able to time-travel, though, there's no telling what would have happened—who would win a Spinosaurus vs. T. rex fight might depend on the strength of the individual dinosaurs.