Gamera
...I believe in one of the Jurassic Park movies they give them a chimpanzee level but it's pretty much over-the-top Hollywood stuff there.
That was actually Crichton's own description, in his original novel. He based it on the research you and I have mentioned, about possible brain volumes, and then extrapolated a little. If I remember, he mentioned in some comments or interview that there are examples among birds today of unusual intelligence--I think he mentioned parrots--and so, it was reasonable (and important to the plot) to make those relatives of birds intelligent.
I read the novel when it was first published, and was so taken with it, that I read it straight through in a day. Crichton really wove the latest paleontological research into the story, along with other technology, making it very believable. And when I read the book, I thought to myself, "Boy, wouldn't this make a great movie, if only they can figure out how to animate the dinosaurs convincingly!" When the movie came along, I was disappointed, because Spielberg really changed the story (Hammond should have gotten his comeuppance, for example. Doctor Grant actually liked kids, too). I thought to myself, "If they took out the humans and just left the scenes with the dinosaurs, it would be pretty cool." And then a couple of years later, the BBC produced "Walking with Dinosaurs", which did pretty much that, a Mesozoic Mutual of Omaha's Wild Kingdom, as it were.
Regarding the T-rex, if I'm not mistaken, their brain casts suggest that the area of the brain governing smell wasvery well-developed. That, along with the structure in their nostrils, suggested that they had a tremendous sense of smell, and may mostly have scavenged, rather than to have hunted actively. We don't like that idea, because it's cool, scary, to think of that animal running down prey. But in terms of biology, it's a lot more efficient and safer to the animal, to scavenge. (Thanks to Jack Horner's books for that info, it has always stuck with me).