It's definitely a roll of the dice.
On average, for the past 20+ years oil has been cheaper than natural gas or propane. In the past 2 or 3 years we are seeing a shifting where natural gas is the cheapest heating source and oil and propane are about equal.
Propane is not a more efficient fuel, however.
1 gallon of propane will generate 91,600 BTUs
1 gallon of heating oil will generate 138,000 BTUs
The difference is that the propane fired burner will typically operate at a higher rate of efficiency than the oil burner so that tends to net out the greater heat capacity of oil.
There was a propane shortage in the Northeast earlier in the winter due to a closed terminal in Selkirk, NY, so prices increased. That problem has been alleviated now so prices have moderated.
If I were building today I would probably go with propane.