First of all, no dog (or cat) will ever be vegan. It's a really silly term to use when we are talking about what we as their guardians feed them.
It's a "plant-based diet".
Both animals can thrive plant-based, but of course with cats it's important they get the taurine etc which usually comes from animals (but can be synthesized also. There are some successful plant-based cat foods out there nowadays.
But both will do what many animals do. i.e. Hunt and kill. They will also gladly accept non-vegan items if offered.
So, neither will ever be "vegan".
I might be being pedantic, but I find this quite irritating "My dog is vegan"...NO HE ISN'T, YOU ARE FEEDING HIM a plant-based diet.
By the way, we have a small dog. And mainly because my family is not vegan, but also due to his insane fussiness and lack of plant-based options in the area, he eats standard dog-food
When I say fussy...He doesn't like any standard dog-treats. I bought him some (quite nice looking) plant-based chews...he sniffed one and looked at me as if to say "what the **** is that?" and walked away.
The only saving grace, if at all, is that he weighs like 6 or 7 kg and doesn't eat much.