The physical properties of the two gases are very similar, and when regulated to the correct pressure, they will perform almost identically. However there are some important differences.
Of the two gases, Butane has the most advantages.
It is less toxic and so can legally be used and stored indoors. Litre for litre, it contains around 12% more energy than Propane and so you can squeeze more running time into the same sized bottle. (Butane is heavier than Propane though, so weight for weight it's a pretty close call.)
Butane also burns cleaner than Propane (although this isn't normally a serious issue in caravanning.)
Finally, while it's not strictly a property of the gas, Butane canisters generally use clip-on type connections. These are far more convenient than the Propane screw type connections, especially if you swap bottles around regularly (as you might if you also use your caravan bottle to run a barbecue.)
Conversely, Propane has only one advantage over Butane - but it's a big one!
In order to be usable, the liquid in the bottle must be able to boil into a gas. In the case of Butane, this will happen at any temperature above -2C, whereas with Propane, this figure is much lower, at -42C. In the real world, it's not so clear cut. Whenever some of the liquid boils into gas, the remaining liquid cools. It is therefore possible for the temperature of the liquid to drop to several degrees below ambient. This can easily prevent a Butane canister from producing a useful gas supply, even when the outside temperature is several degrees above 0C. A compromise can be reached by mixing Propane with Butane, but as far as I'm aware, none of the UK 'big bottle' suppliers actually do this. The small gas cartridges that are produced for camping stoves and gas lamps are often Propane/Butane mixes. So choosing the right gas pretty much boils down to whether you need to use it in freezing (or near freezing) conditions. If this is likely, then Propane is a must. If not, then Butane has the edge.