curi: The trait that differentiates humans from non-human animals, in a veganism-relevant way, is (general, universal) intelligence, which is the ability to learn (aka create knowledge), which is the ability to do evolution of ideas within one's mind.
This is a binary trait, not a matter of degree.
This is not a complete explanation, e.g. it doesn't say how that trait relates to other issues vegans may bring up like consciousness or suffering.
Vegans: What about mentally handicapped people. If they have less intellectual capacity than a cow, is it OK to kill them?
curi: Yes, in principle. They're (by premise) on the wrong side of the intelligence/non-intelligence asymmetry.
However, we should begin our discussion with cases which are easier to understand and potentially agree about, not hard cases or edge cases. If you understand and agree with my way of differentiating most humans from cows, then it'd make sense to discuss edge cases in detail.
Vegans: How do you tell if a normal person or cow is intelligent?
curi: Primarily behavior: people have intelligent conversations, write blog posts demonstrating that they understand TV show plots, act according to learned jobs skills, develop new science, etc. That is best explained by knowledge the person created in his mind rather than by genetic knowledge. Animals behave in simplistic, algorithmic ways which are best explained by the knowledge in their genes.
I think careful analysis of animal behavior, and trying to differentiate it from the capabilities of stuff like video game enemies and self-driving cars, is one of the more productive ways to continue this discussion. People have strong intuitions that animals are somewhat intelligent and are clearly different, in terms of intelligence, than current robots and "AI" software algorithms. Relatedly, people believe intelligence is a matter of degree. Looking at rigorous information of animal behavior, from scientists, and carefully considering the simplest ways it could be achieved, can be informative.