Transport-related activities represented 34% of the total carbon emissions in the UK in 2022 and heavy-duty vehicles (HGVs) accounted for one-fifth of the road transport greenhouse gas (GHG) emissions. Currently, battery electric vehicles (BEVs) and hydrogen fuel cell electric vehicles (FCEVs) are considered as suitable replacements for diesel fleets. However, these technologies continue to face techno-economic barriers, creating uncertainty for fleet operators wanting to transition away from diesel-powered internal combustion engine vehicles (ICEVs). This paper assesses the performance and cost competitiveness of BEV and FCEV powertrain solutions in the hard-to-abate HGV sector. The study evaluates the impact of battery degradation and a carbon tax on the cost of owning the vehicles. An integrated total cost of ownership (TCO) model, which includes these factors for the first time, is developed to study a large retailer's HGV fleet operating in the UK. The modelling framework compares the capital expenditures (CAPEX) and operating expenses (OPEX) of alternative technologies against ICEVs. The TCO of BEVs and FCEVs are 11% to 33% and 37% to 78% higher than ICEVs; respectively. Despite these differences, by adopting a longer lifetime for the vehicle it can effectively narrow the cost gap. Alternatively, cost parity with ICEVs could be achieved if BEV battery cost reduces by 56% or if FCEV fuel cell cost reduces by 60%. Besides, the pivot point for hydrogen price is determined at £2.5 per kg. The findings suggest that BEV is closer to market as its TCO value is becoming competitive, whereas FCEV provides a more viable solution than BEV for long-haul applications due to shorter refuelling time and lower load capacity penalties. Furthermore, degradation of performance in lithium-ion batteries is found to have a minor impact on TCO if battery replacement is not required. However, critical component replacement and warranty can influence commercial viability. Given the high costs, we propose financial incentives and vehicle tax reforms to reduce costs of critical components that will encourage the roll-out of zero emission HGVs.