Just a reminder that this forum is for medical students only. General questions should be posted on the premedical or general board, where everyone will be able to see them and respond.
MD's and DO's get the same training and the same priviliges. DO's also get training in osteopathic manipulation, and tend to focus more on treating the patient as a whole rather than just the disease. Although, to give allopathic schools credit, a lot more of them are moving towards patient centered medicine. In most of the primary care fields (peds, FP, IM, OBGYN) I believe that DO's are seen as equal to MD's, but I have heard of DO's facing discrimination of the type you talked about in fields such as surgery, ortho, etc. I think this is because DO schools tend to accept more non-traditional applicants and are more flexible, and look beyond the scores a bit more, so their average gpas and mcats aren't as high. This makes some people believe that DO students aren't as capable.
Research it some more, apply to both types of schools, talk to DO's and MD's. You have lots of time to decide.