I'm not quite sure how a boiler can be efficient or inefficient. It seems like for every watt of power going in, I get one watt of heat out. That's basic thermodynamics. If heat doesn't make it into the water, it still ultimately heats my house.

Perhaps language issue?

My boiler heats the water for my radiators which heat my house. That's not the same as my hot water tank, which heats running hot water. Here, where modern ones do tend to leak less heat into the air, and these do have a limited lifespan as the tank corrodes.

Can you explain? I feel like the only way I could go up in efficiency is if I sucked in heat from the outdoors with a heat pump.