I have used both, and when set up properly, they both seem to do just fine.
For me, propane is a little more difficult to set up, beause I grew up using acy and then we kinda inherited a set of propane torches, and it takes a while to get used to.
I was always taught to set up the oxy/acy by starting with just acy on, light the fire, and then turn it down just until the flame comes back into contact with the tip. Then add oxygen just until the inner blue cone dissappears. Takes about 2 seconds to set up and cuts like butter.
If you try the oxy/propane this way, it wont cut anything but sheetmetal. Propane, I leave the propane only flame about 1/4" off the tip, and add oxygen until the inner blue cone dissappears, and then a little more oxgen. For me it is just a little more difficult to set up. Propane deffinatally uses more oxy, but everyone says that the cost difference between propane and acy is enough to make up the difference.
I have also read somewhere that the propane has more BTU's farther away from the tip than acy. which makes it better for cutting really thick materials, but the acy is a hotter burning gas, and it doesn't take as long to pre-heat on the thinner stuff.