If they were smarter than us there would definitely be some human hunting going on, but they'd be too thirsty for knowledge and smart about conservationism to wipe us out completely.
They would want to study the stars, poetry, art, the sea, develop religion, drink booze. All that would require a lot of time and effort.
They might try to corral us into herds with fences... But good fuckin' luck kitty how you goona hold a hammer?
Even if they were smarter, humans have the tactical advantage of being able to fashion weapons and defenses while a tigers' just going to lay about half crocked on burboun. It's doubtful that humans would enter some sort of servitude of the big cats too, since we can't speak the same language. Imagine a kitty trying to get us to drive it somewhere, all pawing at the door, jutting his chin toward the car.
We'd be like:
"kitty I don't get what you mean."
And then he'd get all frustrated and be like "rooar! mmeeeeoowwww Roar!"
Yet still we shrug, shaking our heads, declaring:
"yeah you're not helping your case bro, I don't understand you... wanna chase a laser pointer instead?"
Game over son. Game over.