Sadly I don't think so. Humanity had two things going for it that allowed it to evolve into the game-changer they became; an incredibly high brain-to-mass ratio and opposable thumbs. Brain size plays a huge role in determining the cognitive capabilities of a species (to the point we can extrapolate about long-dead species like Troodons just by comparing their brain size to modern-day ancestors like birds) and opposable thumbs gave us the dexterity necessary to create tools and interact with our world however we see fit. Cats and dogs lack several of the biological factors that would spur a species towards evolutionarily advancing their intelligence to the point of true sentience.
Now, if humans had never evolved and I had to pick who might have taken over, I'd say octopi, on a hypothetical Earth that was entirely covered in water. They have big brains, prehensile tentacles, and have been observed creating tools, solving complex puzzles, and forming strong emotional bonds with their handlers. In another timeline I could totally see them as having taken over the planet instead of us.
