Propane provides more units of heat (BTUs) per unit of volume at a given pressure than natural gas by about 2.5 to 1, but propane is more costly in most areas served by natural gas distribution systems. Most gas apliances use a different orifice for propane than for natural gas, check with the appliance manufacturer for more information about suitability of your choice of gas for any particular appliance.
Propane is heavier than air while natural gas is lighter. This can be important to know if you "smell" a leak and you know which gas is in use. Both are colorless, odorless, and tasteless and both have stuff called methyl mercaptan added to make leaks detectable to the human nose, that's why they smell the same.
Propylene burns hotter than propane while providing about the same calorific value (same BTUs) as propane. This is not the same as MAPP gas, which is known chemically as methylacetylene-propadiene - more commonly called MAPP gas. MAPP burns cooler than acetylene, hotter than propane, is can often be purchased for less than either. To the best of my knowledge MAPP is stable and does not require dissolution in acetone as does acetylene.
You can google these terms and get some very detailed information in a hurry if needed.
-Mondo