Generally speaking, creatures evolve to meet the specific conditions of their environmental niche, and the less overlap there is, the less "friction" or com[petition between the species. Carnivores in the African savannah generally specialize on a particular type of hunting method or prey, but even then there are enough areas of overlap so we see things like lions and hyenas fighting over prey or driving each other away from kills.
Humans may be a special case, since Homo Sapiens can use intelligence and technology to adapt to any earthly environment (the Ancestors did this with just wood and stone tools and fire, literally walking around the world and not letting small things like megafauna, mile high glaciers or oceans stop them). Interestingly, only Homo Sapiens remains from all the various hominid species that co existed with us, suggesting that there can be only one species in our niche. The Ancestors may not have exterminated them, but simply out competed Neanderthals, Denisovians and other possible cousins in any environment they shared. We know the Ancestors were the original party animals, since we still carry small amounts of DNA from our hominid cousins in our DNA.
This suggests that if we shared the world with other intelligent species, they would have to live in entirely different environmental niches, such as whales and dolphins.
For the intelligent dinosaurs, many of the same factors would apply. Intelligent dinosaur species might coexist in different environments, and the interaction between them might resemble encounters with spirits - the beings from the "other places" behave in interesting and amazing ways, and can sometimes be enticed to trade unique and unusual items, songs or "art".