They don't always tend to be fully funded so I would assume they aren't as competitive MD/PhD programs. Plus (and this is me reaching since I'm not uber familiar w/ all the intricacies of the DO), the nature and support structure of the DO/PhD doesn't make it the optimal training path for the dual degree.
I'm not aware of any DO/PhD programs that advertise full funding. Take away the funding, take away the competitiveness. The general rule of thumb is that if there is not full funding, it's just as competitive as getting into the medical school would be.