I shadowed (and still do) a DO for well over a year, about 4 hours a week. I used her letter when applying to DO schools. In my acceptance phone call, they made the point that my letter from the DO I shadowed had a big impact on my acceptance. But as stated above, it is meaningful if the physician knows you pretty well, as was the case in my position. So it can make a big difference, but it is obviously not a necessity. Good luck!
Edit: To your original question, a letter from a DO compared to an MD won't make a difference. I haven't seen doctors show discrimination towards the different degrees, I think it's mostly a pre-med bias.