Heating cost: gas versus mazout

There are too many variables here to really make a definitive statement.

A huge factor will be the age and efficiency of your existing boiler. A new boiler whether gas or oil will be massively more efficient than a 10 year old one, and even more vs a 20 year old one.

Also, are you connected to the gas main in the street, or do you need merchant gas delivered to a tank at your house.

If you are in a smaller house, have access to gas in the street outside your house and buy a new combination boiler, that is by far the most efficient and cost effective way to heat.

I had oil heating with a 20 year old boiler.
I converted to gas - supply in the street - and reckon to have saved enough to have paid for the conversion in four years.
Obviously the costs of both oil and gas vary from month to month so there is no guarantee that I could do the same conversion today and be showing a profit in the same time. Also, of course, the fact that my boiler was so old made the saving fairly quick.
Strictly on running costs, gas is more efficient than oil but whether that will always be so and how soon a conversion will be paid back is pure guesswork.

Gas. Oil is due to start being phased out soon in certain areas.