Proposed sustainable transition pathways for moving away from natural gas in domestic heating focus on two main energy vectors: electricity and hydrogen. Electrification would be implemented by using vapour-compression heat pumps, which are currently experiencing market growth in many countries. On the other hand, hydrogen could substitute natural gas in boilers or be used in thermally–driven absorption heat pumps. In this paper, a consistent thermodynamic and economic methodology is developed to assess the competitiveness of these options. The three technologies, along with the option of district heating, are for the first time compared for different weather/ambient conditions and fuel-price scenarios, first from a homeowner’s and then from a whole-energy system perspective. For the former, two-dimensional decision maps are generated to identify the most cost-effective technologies for different combinations of fuel prices. It is shown that, in the UK, hydrogen technologies are economically favourable if hydrogen is supplied to domestic end-users at a price below half of the electricity price. Otherwise, electrification and the use of conventional electric heat pumps will be preferred. From a whole-energy system perspective, the total system cost per household (which accounts for upstream generation and storage, as well as technology investment, installation and maintenance) associated with electric heat pumps varies between 790 and 880 £/year for different scenarios, making it the least-cost decarbonisation pathway. If hydrogen is produced by electrolysis, the total system cost associated with hydrogen technologies is notably higher, varying between 1410 and 1880 £/year. However, this total system cost drops to 1150 £/year with hydrogen produced cost-effectively by methane reforming and carbon capture and storage, thus reducing the gap between electricity- and hydrogen-driven technologies.