Man no offense but you really are against the general consensus of what would happen if a tyrannosaurus rex and Spino actually encountered eachother in real life.
The t-rex has been shown to have about 3000lb more muscle force, it was far more intelligent, it had forward facing eyes which is a big advantage in itself.
It had far better vision, and actually the complete opposite of what you say is true, it was a predator first and opportunistic scavenger second. T-rex would compete with eachother for prey, and take on dangerous prey, the spino ate fish... It was a specialised animal for hunting fish, the rex was specialised for biting through the bone of giant herbivores with crushing power.