Natural-gas heating is usually preferred because it is more-convenient:
less-maintenance after installation, continuous-fuel-delivery, and less-smells/soot.
Natural-gas can share chimneys with wood-fireplaces/stoves,
whereas heating-oil & wood-fireplaces/stoves should NOT share chimneys.
The total-cost-of-ownership can go either-way depending on supplier/vendor-costs/prices.
Improperly-maintained-boilers can explode with either-fuel;
natural-gas-leaks can be EXPLOSIVE,
while heating-oil is just-flammable.