I know that Wisconsin, Minnesota, and Colorado State also have dual DVM/MPH programs. Iowa State has one, too. (Well, it's in cooperation with University of Iowa, so maybe that was the U of I that you listed.) Also, Davis has their MPVM program, which you should check out. If you're less interested in the human public health side of things and more interested in direct animal health applications, the MPVM might be more appropriate. (This is my impression, but I was actually just discussing this with a DVM who did the MPVM program, and she said that was her precise reason for doing the MPVM over an MPH.)
I don't know if it's harder to get into the dual degree program, but I don't think it necessarily would be. Unlike the DVM/PhD programs were there are very few seats, the MPH programs seem to have the capacity to handle many more students. (But I could be wrong here.)
Some things to think about include whether you can complete both degrees in 4 years or whether it will take an extra year. (Iowa State, K State are both in 4 years; Wisconsin and Davis require an extra year to finish their programs.) Also, I know Iowa State has a tuition agreement with U of I where their students pay less (I am a little sketchy on all the details) so the MPH program comes out to only an extra $8-9K (well, using 2007-2008 tuition rates). A pretty good deal.
Also, it seemed to me that all of the schools I visited had the option to apply for the MPH program in your first (or even second) year of vet school without losing any time. This leaves me wondering what, if any, benefit there is to applying to both programs at the same time. In fact, I liked the fact that I could do a year (or so) of vet school and then decide if I still thought the MPH was what I wanted to do. Some schools with both programs also allow you to take MPH courses as electives while in vet school. (I've been told that Davis does this, and I asked about it at WI and they seemed willing to accommodate this type of thing.) That's another aspect that makes me think it could be better to wait, test things out in vet school, and see if you still want to do the MPH.
There is also reputation of the MPH school to think about. One of the public health vets that I work with told me that, in her experience, unless you've got your MPH from Harvard or Johns Hopkins, that basically no one cares from where you received the degree. But from looking into some of these programs, I did get the feeling (my personal opinion and for what I'm interested in) that they were of varying strengths. I've also heard really great things about Minn's MPH program.
Ok, those are my long and rambling thoughts. PM me if you'd like to talk about this more. 🙂