The most important thing that you need to know is the energy source of heat pump as well as furnaces. Furnaces can run with the help of electricity but they mostly run on fossil fuels like natural gas or heating oil. Hence, in order to use furnaces you need to have availability of either natural gas or heating oil. On the other hand heat pumps run only on electricity and so there is no need to have the availability of heating oil or natural gas.
As far as the energy efficiency is considered, heat pumps are more efficient than furnaces in terms of energy consumption and heat production. In case of a furnace, the Annual Fuel Utilization Efficiency or AFUE reveals its efficiency while in case of heat pumps it is typically the Heating Seasonal Performance Factor that tells about its efficiency. However, it needs to be mentioned here that heat pumps though more efficient than furnaces in terms of heat production yet they are not a much suitable option for places where the temperature falls below freezing. Thus, in such a scenario furnaces are a better option.
Furnaces generally last more than heat pumps. Mostly, it is seen that almost after running for 15 long years a furnace needs to be replaced but in case of heat pumps, the average life span might be around 10 years. Nevertheless, for HVAC systems it can be quite difficult to predict the exact number of years for which it will run.