Building on Erin's answer (which I upvoted): Vets will have tendency to rely on what they see instead of what the patient tells them, which may be an asset in an emergency.
Anatomy and physiology of mammals is similar enough that much of what applies to animals can also be applied to humans.
As Amadeus points out (I did not upvote him because I think conclusions he draws are not pertinent) Vets are much more used to consider their patients "expendable", so some finer (and decidedly all "cosmetic") aspects would be lacking.
Another point favoring Vets in respect to "real" M.D. (and to keep in mind in the plot) is a lower degree of specialization; essentially farm animals and pets (there's more than that, but majority is there), while human medicine has become fractionated in such a high number of sub-sub-sectors it's very likely a modern doc would be almost useless for at least two reasons: his knowledge is restricted and thus probably case at hand lies outside it (with possible exception of First-Aid M.D.s) and he is too spoiled, relying heavily on Lab tests and other exotic specialistic exams which might not be available.
A thing a Vet is better to learn fast is humans are much less resistant than animals (even house pets) so they must be treated with more precision (drug dosage, suture points, ...) or they'll break.
Everything I wrote above and all I will write below is from my personal knowledge and experience and is thus limited, in particular it's geographically and culturally localized to Europe, in general, and Italy, in particular, which is where I live and work. I strongly suspect things may be very different elsewhere.
I don't know if this is the recommended way to answering to other posts (see below); please redirect me as needed.
As there has been an exchange of comments with @Amadeus I feel like I need to clarify my position.
I am specifically speaking about M.D.s as we averagely find in Europe, I'm pretty sure nothing of this would apply (as an example) to someone operating in a small hospital in some sub-Saharian village.
Medicine, in the Western countries, has progressed impressively in the last 50 years (that's the period I witnessed, being slightly over 60), as many other things, including computers and transportation.
The latter is particularly important because it opened the road (pun intended) to the switch, in Italy it happened in 1974, to the abolition of the so called "Medico Condotto" who was responsible for sanity in a neighborhood assigning this responsibility to nearby hospitals, rationale behind this was road system was good enough to allow fast intervention even from a reasonably longer distance.
For Medicine this was an epochal change because it shifted responsibility from a single individual (however supported) to a "structure" where many individuals cooperated, but none was alone.
All this lead to a better services (up till current crisis where financing has perilously dropped, but that's not relevant here), but also to fragmentation of knowledge, to the point that, since 2001, it is possible to become M.D. without any knowledge in First Aid.
Similar path was followed by pharmacists; I remember very well, when I was a kid) staring for hours to the village chemist (a friend of my father's) weighing and mixing and diluting and compressing and ... whatever. Nowadays perhaps a Pharmacy in ten (at most!) will accept to do Galenic preparation (and most of them sub-contract others to do the real job) and pharmacists, after years of studying chemistry and the like are reduced to the status of "high level sales clerk" who never used their knowledge to do anything more "practical" than discerning two boxes contain the same thing under different names.
Vets, OTOH, are following the same route, but they are very late and thus, if it is true we see some "vet clinics" (mainly for pets) which are structured like hospitals (with comparable set-up and prices), it is also true most of them operate alone, often with very low-tech equipment, a much restricted array of instrumentation and drugs and less (if any) lab tests.
Speaking about blood (or whatever) test labs: they followed the same path, with the "real work" done by machines, so that analysts are more or less tending and calibrating machines they would hardly be in position to replace personally.
While I'm not trying to belittle the gigantic steps done by medicine in the last 100 years, I see that it has become increasingly dependent on a wide organization and in a post-apocalyptic scenario the very first thing breaking down is exactly organization; this means:
- Machines would break down and it would be increasingly difficult to get replacements.
- Supplies will be in short availability and would have to be substituted with "equivalents" (if and when available).
- The doctor would be alone, possibly with whomever he managed to train.
- The pharmacist would have to actually prepare the drugs, possibly resuscitating whatever knowledge about medical plants.
- Herbalists would become in great demand (not the ones we see selling herbs coming pre-packaged from exotic places, but people able to harvest herbs in the woods and/or to grow them in the backyard).
- Lab analysts would restrict a lot their capabilities and would be forced to do things personally, including gathering supplies.
In this condition, for the sole reason of being already nearer to these (bad!) conditions, I believe a Vet would be immediately much more effective than a generic M.D. and infinitely more effective of an old specialist (who had the time to forget anything about general medicine he learned so much time ago).
In a reasonable amount of time (few years) I believe a young generic M.D. could adapt and learn to be what's needed in the mutated conditions, possibly surpassing Vet abilities.