Well, yes and no.
My understanding (and I can't point to a written source, but it is "common knowledge" among at least my bioanthro colleagues ;-) is that for medical school the success rate for bioanthro majors is higher than for biology majors, provided that you have taken the basic math, chem, & physics courses (a bioanthro major at UCSD pretty much has to take biology too, so that's a given). The reason is twofold: First, medical school admissions committees are looking at thousands and thousands of applications from biology majors; bioanthro is at least a switch and makes them think for a moment. Second, there is increasing attention to sociocultural factors in medicine--understanding the patient, all that touchy-feely stuff-- and in an evolutionary perspective on human health and disease; bioanthro does both of these things better. The one thing that could count against a bioanthro major would be the perception that you majored in bioanthro to avoid o-chem because you can't do the science. There is plenty of information floating around about medical school admissions requirements, so you're on your own for details.
For veterinary school I wasn't sure, so asked a colleague at UC Davis' vet school. The picture is pretty much the same: if you've had the basic science and done well, bioanthro is no disadvantage and would in fact be an asset if you were expressing an interest in primates--your interest would be "verified" by your coursework. For wildlife vet medicine, ecology courses are important as well (these of course could be part of either a bioanthro or biology major); for standard domestic animals the specific courses aren't so important (but experience in private practices is very important). For UC Davis vet school (one of the best, with links to the San Diego Zoo and CRES) you want to shoot for at least a 3.4 cumulative GPA (3.2 in the required science classes and 3.6 for the last 65 units or so) and GREs at least in the mid-80th percentiles. Your personal narrative, vet experience, evidence of real concern with animals, public service all are looked at closely also. For more information and a list of course requirements, see for example the admissions info pages for two of the top schools, UC Davis and Tufts University.
So the bottom line for both: provided that you take (and do well in) those hard-science prerequisite courses like chem and math, all else equal bioanthro is at least "as good" and may have some real advantages. The difference between biology and bioanthro is that the biology degree guarantees you've passed those prereq courses, whereas a bioanthro degree does not in itself demonstrate ability to do well at so-called "hard science" areas. If your GPA is average, it's a gamble: bio degree confirms you can do the science (but you're just another average bio applicant); bioanthro catches the eye but could be interpreted as "avoided all the hard science possible and still only an average GPA" which is not going to help. If your grades in chem/math/physics are good, then all else equal bioanthro is probably a plus.
Bioanthro is not "an easier back door" to med and vet school; it is another (and in some ways better) front door.
Please note:These comments are about the merits of the two majors in general and are not intended to be an evaluation of UCSD's bioanthro vs. biology majors per se. Fact is, that gets into fine-grained details of each program and I just don't have any concrete data on acceptance rates for UCSD students of the two majors.