There is a remarkable difference in the time period of human intervention, for one thing. Dogs for around 30,000 years versus cats for 9,000.
There are ten times more dog breeds than cat breeds, almost entirely due to humans.
I'm trying to find for reference a recent study of cats' genome [※] that also mentioned how today's house cat is not much different genetically speaking from primitive feral cats, whereas as already said, plenty of dog breeds have never even existed in the past and are completely a product of human driven genetic selection.
( There ARE cat breeds also a product of human intervention, of course, but not in the numbers and variety of dog breeds. )
Edit : May as well add, human selection of dogs has altered them in fundamental ways. Selecting for co-habitation, so they don't attack farm animals, but protect them instead. Selecting for intelligence, so they can obey specific commands. Selecting for strength, so they can pull and carry. Etc. Most selection done with cats has been purely for aesthetic reasons, leaving behaviour aside.
[※] Edit 2 : https://www.sciencedaily.com/releases/2014/11/141110161042.h...