In terms of realism, I think dinosaurs are unlikely to compete well with mammals. In our imaginations, bigger is better and so of course huge dinosaurs would win out over smaller creatures -- but evolutionarily, land animals have mostly been getting smaller.
If they could survive, I think they'd have a similar effect on societies as elephants and bears - respected and painted about - but still hunted and killed.
I think your "realism" is just class bias. Dinosaurs competed with mammals for about 150 million years, and mammals never even got a foothold in any of the niches held by dinosaurs.
Also, it's not true that animal have been getting smaller. There were huge dinosaurs in the late Jurassic as well as in the Late Cretaceous, separated by almost 100 million years. Probiscideans are the largest terrestrial mammals throughout the following Cenozoic, and were truly huge by 20 million years ago (deinotheres), but most of the largest species were from the last few million years, including perhaps the largest land mammal of all time (
Palaeoloxodon namadicus). Not to mention that the largest animal of all time exists today (the blue whale, and a dozen other extant species are spectacularly huge as well, even by the standards of their cetacean ancestors).
You're probably thinking of the size shift between the Age of Dinosaurs and the Age of Mammals. Which is real, but seems to be related to reproductive strategies and biological limits, not a trend toward smallness. There are limits on how big you can get, when you give birth to live young and provide extensive parental care. That's why newborn elephants, giraffes, and whales are big. Contrast that with 100 ton sauropod dinosaurs, who hatched from eggs smaller than an ostrich's.