Sustainable transition pathways currently being proposed for moving away from the use of natural gas and oil in domestic heating focus on two main energy vectors: electricity and hydrogen. The former transition would most likely be implemented using electric vapour-compression heat pumps, which are currently experiencing market growth in many industrialised countries. Electric heat pumps have proven to be an efficient alternative to gas boilers under certain conditions, but their techno-economic potential is highly dependent on the local climate conditions. Hydrogen-based heating systems, which could potentially utilise existing natural gas infrastructure, are being proposed as providing an attractive opportunity to maximise the use of existing assets to facilitate the energy-system transition. In this case, hydrogen can substitute natural gas in boilers or in thermally driven absorption heat pumps. Both heating system transition pathways may involve either installing new technologies at the household level or producing heat in centralised hubs and distributing it via district-heating systems. Although the potential of hydrogen in the context of heating decarbonisation has been explored in the past, a comprehensive comparison of electricity- and hydrogen-driven domestic heating options is lacking in literature. In this paper, a thermodynamic and economic methodology is developed to assess the competitiveness of a domestic-scale ammonia-water absorption heat pump driven by heat from a hydrogen boiler compared to a standalone hydrogen boiler, a classic vapour-compression heat pump and district heating, all from a homeowner’s perspective. Using a previously developed electric heat pump model, the different systems are compared for various climate conditions and fuel-price scenarios under a unified framework. The coefficient of performance of the absorption heat pump system under design conditions and the total system cost are found to be 1.4 and £5400, respectively. Comparing the annualised total costs of the options under consideration, it is shown that, assuming the future price of hydrogen for domestic end-users can be below 0.12 £/kWh, absorption heat pumps and hydrogen boilers can become competitive domestic heating technologies, and otherwise, electrification and the use of vapour-compression heat pump will be preferred.