If you don’t live in a hot climate, many heat pump water heaters take heat from indoor air. Be aware of that - you’re heating air, then moving that heat into the water tank. It really drops efficiency. But they’re almost certainly a lot cheaper to run long term than paying for oil deliveries! They’re not necessarily cheaper than gas, because gas is just so cheap. I’d be wary of replacing a working system, because it’s probably not going to break even, but check for incentives that might help with the cost.
If you make the investment, a water softener could be a good investment. Draining/flushing and maintaining the anode rod is a big factor in longevity.
Tankless is ok, but it burns oil or you need pretty serious electric service. One downside is that the hot water piping doesn’t get the heat transfer from the tank of hot water so the whole pipe length cools fairly rapidly; 1hr between showers and you need to run the tap for a while.
I believe that a heat pump boiler should have backup electric heating elements that kick in when there’s high demand or if it is too cold for the heat pump to keep up.