That’s a contentious claim:). Dog brains are larger, but cats have approximately twice the neural density of dogs in their cerebral cortex ( ~300 million vs ~160 million nerve endings ), the seat of memory and learning in humans.
Dogs are undeniably more social, more trainable and better at learning complex tasks. I’d consider dogs to be on average “smarter” than cats, hard as that is to determine objectively. However whether that means they are more “conscious” in terms of self-awareness is pretty hard to suss out.
Yes, my cats understand most of the time, sometimes they just choose to ingnore me. They know the words food, poof (soft food), treats, kiss, hug. One gives me five if i say give me five or give me paw. when they climb up where they aren’t supposed to be. if i say no, they will try to ignore it and as soon as i start counting, they whine and get down. lol. if i talk to them they respond back most of the time. they also know commands like sit.