To reduce the fossil-fuel consumption and the impacts of conventional ammonia production on climate change, green ammonia production processes using green hydrogen need to be investigated. For commercial production scale, potential alternatives can be based on biomass gasification and water electrolysis via renewable energy, namely biomass- and power-to-ammonia. The former generally uses entrained flow gasifier due to low CO2 and almost no tar, and air separation units are shared by the gasifier and ammonia synthesis. The latter may use solid-oxide electrolyzer due to high electrical efficiency and the possibility of heat integration with the ammonia synthesis process. In this paper, techno-economic feasibility of these two green ammonia production processes are investigated and compared with the state-of-the-art methane-to-ammonia process, considering system-level heat integration and optimal placement of steam cycles for heat recovery. With a reference ammonia production of 50 kton/year, the results show that there are trade-offs between the overall energy efficiency (LHV) and ammonia production cost for all three cases. The biomass-to-ammonia is the most exothermic but is largely limited by the large heat requirement of acid gas removal. The steam cycles with three pressure levels are able to maximize the heat utilization at the system level. The power-to-ammonia achieves the highest system efficiency of over 74%, much higher than that of biomass-to-ammonia (44%) and methane-to-ammonia (61%). The biomass-to-ammonia reaches above 450 $/ton ammonia production cost with a payback time of over 6 years, higher than those of methane-to-ammonia (400 $/ton, 5 years). The power-to-ammonia is currently not economically feasible due to high stack costs and electricity prices; however, it can be competitive with a payback time of below 5 years with mass production of solid-oxide industry and increased renewable power penetration.