Our house had an oil furnace, we added an air source heat pump. There are periods in the winter where the heat pump can't keep up, but in the months early and late winter it's all we need. The net result is that it has significantly reduced our oil consumption. Add to that fact it's an A/C unit in the summer, and it's wins all the way around.
The problem is most oil or gas fired heating systems are forced hot water (or steam) so a heat pump isn’t going to help you unless you want a mini-split in every room.
Even if you have ducting for cooling with AC it likely won’t have enough CFMs for heat in the winter unless it was specifically sized that way (but you likely wouldn’t be still using forced hot water or steam in that case).
At 30f - until you exceed 15-15.5 cents per kWh, heat pump is cheaper to run than median oil price.
It’s not that a heat pump isn’t more efficient it’s that if you have forced hot water or steam radiators you are looking at an additional $40K to retrofit forced air ducting to your house. Oh and you still need a solution for domestic hot water, probably you’ll just end up with a resistive heater (or a hybrid/heat pump unit like the Aerotherm but the heat has to come from the room).
https://www.energy.nh.gov/energy-information/nh-fuel-prices
Actually right now #2 heating oil is now somewhat cheaper per MBTU than propane. Also Natural Gas is slightly cheaper than heat pump per MBTU (YMMV on efficiency!)
I’ve never seen propane cheaper than heating oil here!
EDIT: It’s probably worth pointing out that the North East of the US is the largest heating oil market in the world.
The cheapest rate is 38c/kWh, the most expensive is 62c/kWh..