Do you think I should replace my furnace with a boiler?

So, I’ve been wondering about different heating options. I have had a furnace my entire life. I really like the toasty nature of having a furnace, but a furnace is not the most cost-effective heating option. My monthly heating bill has been getting more and more expensive because my furnace has been slowly breaking down. I called my HVAC provider and went through heating options with them. We discussed getting a new furnace with a great SEER (Seasonal Energy Efficiency Ratio) rating. I was on board for replacing my furnace with another furnace but then my HVAC provider recommended a boiler as a heating option. I had never really considered using a boiler before and want your opinion. The HVAC provider told me that the “toastiness” that I enjoy with my furnace will not be present with a boiler. The HVAC provider told me that while a boiler will give me the same level of climate control, it just won’t be as fast as would a gas furnace. My HVAC provider told me that the tradeoff for the toastiness is the energy savings and the money I save from not relying on a ductwork system (furnaces use ductwork, boilers use hot piping). Do any of you have boilers or have any of you used boilers in the past? I have never had a boiler and I’m a little nervous about making that change. Especially since my HVAC provider told me it would be more difficult to switch back from a boiler to a furnace than the initial switch of furnace to boiler. Which do you prefer and why? Is the cost worth it? I would really appreciate your input on the furnace vs boiler issue. Thanks in advance!