Is there more types of dogs or cats?

Since humans are a subset of animals, there cannot possibly be more humans than animals in the world, and if you can think of even one non-human animal in the world, then there are more animals than humans.

Slightly less obvious: there are FAR more non-human animals than humans in the world. For example, there are about three times as many chickens as there are people. There are fewer cattle than people (about 1 cow per every 5 people), but they weigh more, and it's estimated that the biomass of cows on Earth is greater than that of any other single animal species with the possible exception of krill (tiny, but present in truly immense numbers).