Heroin is a faster acting form of morphine. It's been beaten to death, how the acetylation and consequential lipid solubility facilitate the faster crossing of the BBB, but in the end the drugs have the same effects. The main differences are 1) the rush (especially IV) and 2) the intensity of the effects.
Most people (including myself) prefer heroin for the aforementioned reasons. It's also important to realize that insufflated morphine has rather poor BA. If you were to take equipotent doses of both drugs IV (aside from the different rush), you may have a hard time telling which is which.
Also, I don't think heroin feels like oxy. Oxy is stimulating and heroin is so sedating. Just my opinion.