Depo-medro is an injectible. Prednisone is oral. They are the same medication = methylprednisolone. (from what I have been reading.)

The injection should last for about 3 weeks. I think the reason it is better is he gets the large dose at once instead of a pill per day for the 3 week period. But I am assuming. These are not he vets words.

http://www.medi-vet.com/DepoMedrol.aspx

http://www.marvistavet.com/html/prednisone.html