It really depends on your field and fortunate timing than MD/DO.
If you are in a field that is saturated right now, it may be hard to find a job in a particular location, even if you were a Harvard MD trained at Hopkins. If you are in a field that is experiencing a severe shortage (and growing demands), you can get a job almost anywhere (and recruiters will start cold-calling you while you are in training). What is in demand now may not be in demand when you're done with training, and what is not in demand now may be in demand when you're done.
When physician groups are hiring, they want someone they can work with, whom they can trust. Pedigree is one aspect of this, but also "plays well with others?" is also very important (although this criteria is not used much in academic medicine). Outside academic medicine, playing well with other is VERY important.
Academic medicine is different - while pedigree is somewhat important, it's more your CV that you bring (and what research you have done, but more importantly, how much grant money you can bring to the institution). Because academic medicine pays less (in some cases significantly less) than their private practice counterpart, often at the entry level (instructor, or assistant professor) positions, there are openings because they have a hard time recruiting and retaining. And moving up the foodchain in academia requires work (depends on if you're tenure-track or not, research-based or not) ... but promotion will be based on your work rather than your pedigree.
But to answer the original question - whether it is difficult for DOs to get a job compare to MD - for the vast majority of cases, no. The degree/medical school makes fewer differences outside academia - more likely it will be your specialty and location that will play a far bigger role in finding jobs (or not finding jobs)
