ALERT for those with weak constitutions STOP READING THIS POST NOW!!!
Having sadly smelled both a few times too many (a previous carreer in emergency services/ems/fire rescue) I can say with 100% certainty that they are not exactly the same. Both are horrible, and once smelled you will never forget them. The smell of a body decomposing includes the smell of decaying flesh such as that encountered with gangrene. But it also throws in the wonderful fragrant bouquet of all the bodilly fluids, digestive fluids and bodily waste. So the overall smell is diferent. Also unless you encounter the body at a very very early and specific point of decomposition, the smell of gangrene from a living person will be much much stronger and overwelming. I don't know that I could even begin to adequitely describe the diferences, but once you have encountered them, you can sort of tell which is which, provided your nose hasn't simply shut down in protest. In the case of the decomposing body your nose has enough time to say "something is dead", while in the case of gangrene or similar decay you really have trouble staying in the room/house/county long enough to even form that thought.