My 2 cents as a veterinarian who teaches primarily at an medical school and secondarily at a veterinary school.
I do have to admit that the training that MD students get is far more in-depth. Honestly, it just IS. It's on a completely different level - and that's okay. I wish people would stop getting so overly defensive about it. Veterinary training IS broad and shallow. Because it simply has to be due to the number of species we need to learn about. AND THAT IS OKAY.
As an educator, I truly believe that the best and deepest form of understanding disease is being able to go from what is happening on a biochemical level, to a cellular level, to a tissue level, to an organ level, to a clinical sign and presentation level. That is why you understand WHY the disease does what it does, HOW it does it, and WHY treatment xyz is appropriate. On the vet student side, I'm simply not able to take it to that level due to the volume. Vet students primarily need the "Whats" and "How to Fix"es - there is simply not enough room for all the "Whys". Of it there IS room for some Whys, we are only able to skim the surface or go over it once or twice. Whereas medical students also get a MUCH bigger dose of the "Whys" and we can go crazy in depth with the pathophysiology of whatever organ system or disease we are talking about.
Tl;dr: Is medical education "superior" to veterinary education in the overall scheme of things? Of course you can't say that, because it is comparing two different careers. However, the depth of understanding of both 1) general and 2)organ-specific pathophysiology in medical student education is definitely superior -- and I'm talking in general, BEFORE they specialize.